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Optimization Problem #1
Posted by: patrickJMT

Video duration: 433 seconds
Global video hits: 53241

An Optimization is Shown using Derivatives. I have posted another examples as well! For more free math videos, visit JustMathTutoring.com

Related: math, calculus, optimization, problem, derivative, derivatives, maximum, minimum

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Latest comments made on this video:

@XtGu no problem. ...
By: patrickJMT. on 28 Jul 10, 00:45:31
@XtGu no problem. glad u like them.

Great videos, thank ...
By: XtGu. on 28 Jul 10, 00:44:22
Great videos, thank you for taking the time to make these

@Elphiebubble i ...
By: patrickJMT. on 14 Jul 10, 23:34:26
@Elphiebubble i would take it but.... i was watching the news about two days ago, someone sent this old lady a box of chocolates that was a bomb. no shit. happened in houston. crazy crazy people out there. (bites apple... BOOM!)

I feel like I ...
By: Elphiebubble. on 13 Jul 10, 15:05:16
I feel like I should send you a fruit basket or something. There is no way I'd have an A in Calculus if it wasn't for you! Thank you so much!

Thanks, thanks a ...
By: Ritm2. on 04 Jul 10, 22:04:36
Thanks, thanks a lot. A student from Chile.

Thank you ! for ...
By: jedicaptain41. on 24 Jun 10, 14:32:06
Thank you ! for making these videos

@patrickJMT No is ...
By: gastar1000. on 24 Jun 10, 02:32:30
@patrickJMT No is NOT .In a rectangle ,the dimension X must be different of dimension Y . So to solve this problem you also have to consider the approximation of the second value that makes the area minimum as possible. If you are not satisfied with that. Ask another MIT teacher.

x is different from ...
By: gastar1000. on 24 Jun 10, 02:25:27
x is different from y , so certainly can not be a square . because by an square you will find the same area but the dimensions would be different.

You don't use the ...
By: wongIgnow. on 15 Jun 10, 23:38:45
You don't use the chain rule on 2000x to the negative first?

@patrickJMT Oh, ...
By: 3lizza. on 07 Jun 10, 23:19:38
@patrickJMT Oh, sorry, but I thought that a square have all the sides of an equal size. Thanks...

@3lizza a square is ...
By: patrickJMT. on 04 Jun 10, 12:55:10
@3lizza a square is a rectangle

@pec00laa ha, ...
By: patrickJMT. on 04 Jun 10, 12:54:47
@pec00laa ha, thanks!

hey ! every time i ...
By: pec00laa. on 30 May 10, 10:38:32
hey ! every time i look for a video for math21(differential calculus) lessons i always make sure that it's yours. YOU ARE EFFIN AWESOME.

watch out!! x^2= ...
By: hide7890. on 20 May 10, 18:45:32
watch out!! x^2=1000 => Abs(x)=Sqrt(1000) the fact is that, because we're talking about areas, -sqrt(1000) is non-sense and we get rid of it. BUT, in a test, you've got to write it ALL otherwise it's ALL WRONG.

@saltylemorse yes, ...
By: patrickJMT. on 17 May 10, 23:20:27
@saltylemorse yes, in usa we stop using x for multiplication in middle school... i can not remember the last time i wrote 'x' for multiplication!

your videos are ...
By: saltylemorse. on 17 May 10, 23:06:38
your videos are great but i can't help but notice from all the videos i've watched that the methods used in america to do maths is different to in the uk. for example when we're using x we have a special way of writing x so that it doesn't get confused with a multiplication sign - so i take it that is why you use a dot because you just use a normal x for algebra? does that make any sense? i like the way you guys do completing the square - makes a lot more sense that the way i got taught!

@patrickJMT i have ...
By: aznelf13. on 15 May 10, 04:44:41
@patrickJMT i have to agree, in high school, I wanted a career in math , but it was was a joke because it was so simple, but when i got to cal in college, it was such a burden because it is a bore to understand the professors. The only way i really learn cal was from pat with his style of teaching made it so much more simple to understand and much more motivating.

I have a question.. ...
By: 3lizza. on 11 May 10, 01:32:59
I have a question... Is about a rectangle or about a square?

Though it's been ...
By: Sectorsophia. on 08 May 10, 20:23:11
Though it's been said many times and many ways, you are an amazing teacher! I discovered your vids last semester, now this semester it seems like everyone in my calc class watches you. Thanks so much, all the best.

of course, everyone ...
By: linkmarche. on 05 May 10, 22:17:32
of course, everyone knows that the smallest perimeter of a rectangle with a specific area is a square xD

Thank you. My ...
By: etrnlchaos. on 26 Apr 10, 02:35:41
Thank you. My current teacher isn't very good at explaining these concepts, but when you explain it, it seems simple.

You are one ...
By: aparrotslife. on 23 Apr 10, 04:04:53
You are one topnotch math guru! Thanks a million!

Amazing Patrick, ...
By: omarofuae. on 11 Apr 10, 23:38:40
Amazing Patrick, you saved me on my calc test.

thnx! ive been ...
By: catnawal. on 09 Apr 10, 06:17:02
thnx! ive been needing help in this! =] problem is i need to know how to do this but with 3d figures. :/

lol special type of ...
By: plutoend99. on 29 Mar 10, 11:43:30
lol special type of rectangle, namely a square...

Optimization with Calculus 1
Posted by: khanacademy

Video duration: 590 seconds
Global video hits: 32642

Find two numbers whose products is -16 and the sum of whose squares is a minimum.

Related: calculus, optimization, derivative, minimum

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Latest comments made on this video:

good video, but ...
By: gigamuffin. on 20 Jun 10, 22:26:36
good video, but don't forget to test the critical numbers and restrictions on the variables in yor sum formula to determine which value will give you the minimum sum

love you
By: alaazahra. on 12 May 10, 05:41:06
love you

if your REALLY ...
By: getmoreutubeviews. on 06 May 10, 17:14:34
if your REALLY interested in getting noticed on youtube, check out my video. I can get you 100,000 VIEWS in a month or 2, and then it can go viral. Seriously Stop wasting your time with this stufff, all the big promoters are now using mine.

nice. but when you ...
By: XtagdaearthX. on 05 May 10, 01:53:28
nice. but when you did the second derivative test you couldve just used the first derivative and made and S prime number line

THANK YOU THANK YOU ...
By: bonitachica786. on 31 Mar 10, 03:02:00
THANK YOU THANK YOU THANK YOU

If you want to see ...
By: ClassicsOfMath. on 16 Mar 10, 02:38:53
If you want to see Isaac Newton's seething passion, watch "The Invention of Calculus"

@BrendaGoes123 ...
By: FreezingSun14. on 13 Mar 10, 18:38:28
@BrendaGoes123 instead of using that tedious formula, sal just brought down the 256 to be multiplied by x^-1 cuz 256/x=256x^-1. This way he could just use the power rule, not the quotient rule

You're wonderful. I ...
By: murderXmeXsweetly. on 17 Feb 10, 03:26:30
You're wonderful. I can't even tell you how much these videos have helped out.

that is when there ...
By: xyfaer. on 15 Feb 10, 00:00:50
that is when there is a variable on top and bottom of a quotient. in this case it is 256x^(-2)

Thank you so much. ...
By: YOitsNat. on 07 Feb 10, 21:01:43
Thank you so much. you are a great teacher, and you have great hand writting.

it is right, he ...
By: djenne08. on 01 Feb 10, 05:28:09
it is right, he made x sqaured into x to the -2 in order to get rid of the fraction...

@BrendaGoes123 he ...
By: shadowflash9. on 17 Jan 10, 01:57:44
@BrendaGoes123 he rewrote the problem as a multiplication problem (256)x(x^-2) and then he used the product rule which is just the derivative of the first thing times the second thing plus the derivative of the second thing times the first thing since in this case the derivative of the first thing (256) is zero,(thus rendering the entire first multiplication problem 'zero') we are left with the derivative of the second thing times the first thing.

256 IS a function! ...
By: deanaolles. on 15 Jan 10, 17:30:53
256 IS a function! It is a constant function represented graphically by a horizontal line. Since there exists one and only one y value (256) for every x (all real numbers) f(x)=256 satisfies the criteria of mapping from domain to range in a function!

ohh very good.....i ...
By: LuisSlash. on 07 Jan 10, 22:21:19
ohh very good.....i practiced this problems in the UNI (UNIVERSIDAD NACIONAL DE INGENIERIA) LIMA PERU...GBY

256 is not a ...
By: sublimefunk. on 26 Dec 09, 06:57:19
256 is not a function...its a constant. you don't need to use the quotient rule its just a constant times a variable

are you sure you ...
By: BrendaGoes123. on 16 Dec 09, 02:01:08
are you sure you took the derivative right for 256 divided by x squared. isn't the formula f prime of g minus g prime of f over g squared?

wow, calculus looks ...
By: ZeroG004. on 13 Dec 09, 03:09:54
wow, calculus looks difficult. I understand some of the functions but I don't know where hes getting some of his numbers. I wish I was good with numbers =\

You are seriously ...
By: msthickness2012. on 09 Dec 09, 18:55:38
You are seriously better than my Calc1 professor at FMU....Thanks for putting these videos up! You are my lifesaver!

A company makes and ...
By: illmatic33. on 09 Dec 09, 04:00:01
A company makes and sells X digital cameras/week. the weekly price-demand and cost equations are, P=400-.04X; C(x)=2000+160x. (a) What price should a company charge for cameras, and how many cameras should be produced to maximize weekly income? (b) what is the maximum revenue? Can you please solve this word problem? One i see it solved i can figure out the pattern and apply it to the other similar ones i have :-) Thanks

thank you so much
By: MacMacPherson1. on 02 Dec 09, 17:17:20
thank you so much

you are the man
By: speedracer300. on 01 Dec 09, 00:10:00
you are the man

out of his quick ...
By: sasamuraki. on 24 Nov 09, 18:50:16
out of his quick jokes - this has gotta take the cake 'save my electronic ink' - lmao!!!!!!! well apart from the infamous '(s)e^x, i sometimes think about this when i go to bed' - sal, keep up the good work, u share the unselfishness of the late nikola tesla and humorous side of einstein... thanks heaps... save my electronic ink, loool.....

thank you so much ...
By: Xlaxsauce. on 22 Nov 09, 21:46:11
thank you so much this is my biggest problematic unit in calculus

"I should be ...
By: KMedina619. on 20 Nov 09, 16:06:48
"I should be writing 'S(x)'--I shouldn't be lazy with my notation..." Classic... Thanks for the video!

OMG you definitely ...
By: babyphat31. on 16 Nov 09, 23:23:02
OMG you definitely made everything much easier.

Optimization Problem #2
Posted by: patrickJMT

Video duration: 426 seconds
Global video hits: 30816

Another Optimization Problem using Derivatives! For more free math videos, visit JustMathTutoring.com Austin Math Tutor, Austin Math Tutoring, Austin Algebra Tutor, Austin Calculus Tutor

Related: optimization, math, calculus, derivative, derivatives, optimize, austin, tutor

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Latest comments made on this video:

is you answer is in ...
By: romyboy. on 22 Jul 10, 02:11:25
is you answer is in area or in dimension im lil bit confuse i the thought D=2x+2y why is it in D=2xy plz help im confuse

Thank you so much ...
By: hotsum0ta. on 08 Jul 10, 05:00:11
Thank you so much for these videos! They have helped a bunch :D

You have helped me ...
By: LMT9067. on 02 Jul 10, 05:35:53
You have helped me so much as I have been going through the courses to get my math minor and engineering degree. Do you have any videos for partial differential equations? its the last math class I will ever have to take :(

thx a lot!
By: smokingun7. on 01 Jul 10, 02:16:57
thx a lot!

@O0oSorousho0O i'll ...
By: gsharpshooter80. on 28 Jun 10, 02:55:28
@O0oSorousho0O i'll try !

@gsharpshooter80 ...
By: O0oSorousho0O. on 28 Jun 10, 01:35:52
@gsharpshooter80 Same. Watch it again you'll get it. I zoned off a lil'.

can you do harder ...
By: orioles9461. on 17 Jun 10, 21:47:10
can you do harder ones please? these are good but my tests have harder stuff than this.

is it true if you ...
By: jonolollmao. on 15 Jun 10, 15:23:27
is it true if you plug in x for the second deriviative and its >0 then its a minumum point and vice versa? but what about point on inflexion ( =0 ), this confused me

@patrickJMT You're ...
By: Hallucisquid. on 08 Jun 10, 09:03:13
@patrickJMT You're funny =D

thank you thank you ...
By: Tobey7049. on 10 May 10, 05:42:39
thank you thank you thank you x infinity!

thanx man but i ...
By: gsharpshooter80. on 04 May 10, 04:13:06
thanx man but i still suck at this i think im not looking at it the way everyone else is ohh well heh.

Great work Man.. ...
By: rodthelumor. on 01 May 10, 05:25:10
Great work Man.. big Ups to you... you work is definitely most diligent and respectable!

you rock!
By: Manbearpig8900. on 14 Apr 10, 21:18:04
you rock!

patrick man i love ...
By: donreychronic. on 13 Apr 10, 19:39:37
patrick man i love you.

The x there is ...
By: flaco954. on 21 Mar 10, 19:40:11
The x there is actually just the multiplication symbol.

@suckmythach That ...
By: Lucildor. on 12 Mar 10, 06:14:38
@suckmythach That x he wrote there is just a multiplication sign. I know its confusing, I thought the same thing at first! :)

When you are ...
By: suckmythach. on 04 Mar 10, 10:02:59
When you are writing the dimension of the rectangle at 5:51, is that x supposed to be there? x is already defined as the square root of 8/3 right?

Thank you so much ...
By: mambofatale. on 01 Mar 10, 09:32:11
Thank you so much for the patient explanation! I struggled with this problem for 2 days before I watched your video and I finally understood! Doing online calculus is tough, and you really help to give the feeling of sitting in a classroom when it really counts. Thanks again!

tnx mr LEFTY
By: vallakan. on 26 Feb 10, 12:41:39
tnx mr LEFTY

You are helping me ...
By: LBnation30. on 07 Feb 10, 23:51:21
You are helping me so much. Keep up the great work man.

Oh I coulda sworn u ...
By: Jesuskrieger. on 11 Dec 09, 02:52:24
Oh I coulda sworn u said to find area...oops haha. I did get the dimensions, but I went on to find area. Would it be (64sqrt(6))/9 ?

Patrick.... You the ...
By: mxm2010. on 07 Dec 09, 23:06:03
Patrick.... You the man! Appreciate everything you do bro.

Thanks dude. Great ...
By: raghmar. on 03 Dec 09, 22:18:35
Thanks dude. Great stuff!!

You are super ...
By: jdawesallen. on 24 Nov 09, 07:27:53
You are super helpful!!! Thanks!!!!

you explain this so ...
By: JzzdInMyPant. on 17 Nov 09, 07:41:36
you explain this so well i feel like i am cheating :D

AdSense Optimization
Posted by: lockergnome

Video duration: 312 seconds
Global video hits: 101778

live.pirillo.com - How does Chris make a living? By creating content! And AdSense is a great way to monetize that content. Chris gives a community member some free AdSense optimizationtips

Related: adsense, personal, computer, pc, digital, help, howto, how, to, video, callforhelp, call, for, geek, chat, gadgets, chris, pirillo, review

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Latest comments made on this video:

how can i get video ...
By: geebones. on 28 Jul 10, 04:31:22
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For example you ...
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ok everyone just ...
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if your REALLY ...
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my site is ...
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adsense is not ...
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adsense is not going to make you mega bucks, but I make enough to pay for my game server for a month. which is pretty cool for free!

I'm trying to get ...
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Genius.
By: computerclimax. on 28 Feb 10, 16:52:46
Genius.

Optimization Example 4
Posted by: khanacademy

Video duration: 588 seconds
Global video hits: 13699

Minimizing the cost of material for an open rectangular box.

Related: calculus, optimization, derivative

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Latest comments made on this video:

im so shocked! ...
By: jonolollmao. on 15 Jun 10, 17:49:29
im so shocked! that differentiation and max/min points on a graph are so useful to real life!! i can imagine some random guy designing a storage box for a product doing all these workings LOL

lol send me your ...
By: alaazahra. on 12 May 10, 06:02:44
lol send me your address and I ill mail you a calculator bro !

Thank you for ...
By: coffeevampiress. on 01 Apr 10, 13:57:56
Thank you for talking about how you know whether the answer is a max or a min value. That's been a nagging question in the back of my head for a while, how do you know the answer you are getting is really the one they are asking for, but I will try the second derivative on this one... I'm wondering, what would you do if you had to find the cost of the most expensive box?

Great tutorial man. ...
By: GunnergruntC22. on 14 Jan 10, 03:52:12
Great tutorial man. Really helped me out.

Amazing. I'm ...
By: bkisme. on 08 Dec 09, 08:21:18
Amazing. I'm gonna kick the crap out of the 2nd part of my calc test tommorow :D

Awsome tutorials ...
By: hitopachy. on 28 Nov 09, 21:58:56
Awsome tutorials helped me get through calc

why is this shit ...
By: blackhearts8. on 05 Nov 09, 04:07:43
why is this shit soo easy when people explain it?!?!? fuck... but thanks man... very welll done

crystal clear and ...
By: marcusjhung. on 21 Oct 09, 20:22:23
crystal clear and easy to understand, thanks Sal

its soooo much ...
By: angelsarah7. on 18 Jun 09, 02:47:54
its soooo much clearer when you explain it... i kind of understood it before but now i get it without second guessing what im doing.. thank you!

can u write my ...
By: kickit246. on 18 Apr 09, 00:50:09
can u write my final for me tomorrow plz? lol

oh, thanks!!
By: iluvjiyongx3. on 25 Jan 09, 22:03:05
oh, thanks!!

yep, now we know ...
By: Yoshi3003. on 25 Jan 09, 13:36:12
yep, now we know the length, just substitute it in the cost function. That should be the real final answer.

so u just plug x in ...
By: iluvjiyongx3. on 24 Jan 09, 19:35:22
so u just plug x in and add up the base and sides?

He probably forgot ...
By: Yoshi3003. on 13 Dec 08, 13:08:08
He probably forgot that.. since x = 1.65 m so base cost = 2x^2 = 2(1.65)^2 and etc..

the question asks ' ...
By: yeyeye1. on 12 Dec 08, 11:41:05
the question asks 'find the cost of materials' and theres no final answer with a cost...

lol Yahoo Mail - ...
By: brco2003. on 02 Jul 08, 23:56:17
lol Yahoo Mail - you're great

Ohhh I get it now!! ...
By: GoldAK47. on 28 Jun 08, 20:47:02
Ohhh I get it now!!! :) Makes so much sence. BEDMAS. I'm such an idiot. You're a genius. Keep it up

no. It is correct ...
By: khanacademy. on 27 Jun 08, 13:12:05
no. It is correct as done in the video

so I'm right??!!
By: GoldAK47. on 27 Jun 08, 02:38:15
so I'm right??!!

Exponents take ...
By: khanacademy. on 27 Jun 08, 01:13:19
Exponents take precendence over multiplication so 5x^-2 = 5(x^-2) = 5/(x^2), not (5x)^-2

Huh? I don't get ...
By: GoldAK47. on 27 Jun 08, 00:58:16
Huh? I don't get one part. You reduced 10/2x^2to 5x^-2, which means it is 1/5^2 when it really should be reduced to 5/x^2. Did you make a mistake there? (am I making sence :P)??

Optimization Problem #3 - Making a Rain Gutter
Posted by: patrickJMT

Video duration: 621 seconds
Global video hits: 17858

Optimization Problem #3 - Making a Rain Gutter! This optimatization problem involves some trigonometry too! For more free math videos, check out JustMathTutoring.com

Related: math, calculus, optimization, problem, derivative, derivatives, maximum, minimum

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Latest comments made on this video:

@vd853 Remember the ...
By: O0oSorousho0O. on 28 Jun 10, 02:00:54
@vd853 Remember the "Z" pattern in Gr 9 Geometry?

10:01-10:04 You ...
By: O0oSorousho0O. on 28 Jun 10, 01:57:16
10:01-10:04 You sounded funny when u said it lol

@ArrudA666 Yes. Try ...
By: O0oSorousho0O. on 28 Jun 10, 01:44:24
@ArrudA666 Yes. Try testing that eq'n with a calc you'll see the proof e.g. sin^2(0) + cos^2(0) =1 0 + 1 = 1 and sin^2(90degrees) + cos^2(90degrees) =1 1 + 0 = 1

@hsb225623 If you ...
By: webmastertool. on 24 Jun 10, 12:59:30
@hsb225623 If you optimize area for a flat shape, when the shape turns 3d it is automatically optimized for volume.

all four teta ...
By: vd853. on 18 Jun 10, 20:11:52
all four teta angles are equal? how?

Quite the beast of ...
By: jazzysax102391. on 27 May 10, 21:14:00
Quite the beast of a problem

Awesome explanation ...
By: Hackiesacker007. on 17 May 10, 06:39:29
Awesome explanation! Thank you!

I never know what ...
By: PiningSapience. on 09 May 10, 16:07:25
I never know what were talking about in class until I look it up on your site. I'm surviving calculus because of you, thanks soo much!

@darn111 haha
By: gsharpshooter80. on 08 May 10, 21:41:30
@darn111 haha

@gsharpshooter80 ...
By: darn111. on 07 May 10, 19:54:53
@gsharpshooter80 hahaha that's very funny

the two T's on ...
By: RyanEnvy. on 04 May 10, 23:29:21
the two T's on gutter look like Pi! :D

hahah the problems ...
By: gsharpshooter80. on 04 May 10, 04:17:06
hahah the problems looks like an angry face screaming making a rain gutter !

I love you.
By: kyootaay. on 03 May 10, 05:53:46
I love you.

if the 10m of the ...
By: sapphirexsunset. on 01 May 10, 21:57:53
if the 10m of the side-lengths of the gutter werent given - just that the total had to be 30, would using trig or pythagorus be easier? (on the areas/relationship of the triangles - w and h)

@patrickJMT ...
By: FlavouredVitamin. on 28 Apr 10, 06:27:01
@patrickJMT Something we need to ask Freud! You are absolutely amazing!!

wouldnt u want to ...
By: hsb225623. on 26 Apr 10, 04:25:24
wouldnt u want to find volume of gutter? not area

wouldnt you want to ...
By: hsb225623. on 26 Apr 10, 04:24:50
wouldnt you want to find the volume? not area

@patrickJMT lol u ...
By: aznwoowooo. on 16 Apr 10, 03:14:04
@patrickJMT lol u cant have gone thru algebra II without cos^2 +sin^2 =1

couldn't you have ...
By: popcornredbag. on 12 Apr 10, 12:41:38
couldn't you have just used Pythagorean theorem instead of sin and cos? it would have been way easier.

thnxx :)
By: Ufaqueiqbal. on 03 Apr 10, 04:56:52
thnxx :)

I wonder how the ...
By: gespilk. on 09 Mar 10, 23:56:50
I wonder how the solution would look like if instead of gutter we have a canal to dig and we have to minimise the cost of building it. In this case given are the max width of the canal and the minimum throughput of water. The question is what shape would minimise the cost of concrete used to isolate the canal plus what shape would be cheapest to dig (complex shapes are more expensive I think). This is more like a real life engineering optimisation. Could give us some pointers in another video.

I thought that ...
By: gespilk. on 09 Mar 10, 23:24:16
I thought that semi-circle would be the shape that provides maximum volume for a given perimeter. At least that what they tell us is good for space domes (min surface max volume). I could guess the shape of the gutter here is approximation of a circle.

Whoops, one mistake ...
By: DragBag2000. on 03 Feb 10, 04:01:37
Whoops, one mistake. You would actually have to do 90 - arctan(w/h), since arctan(w/h) will give you the measure of the angle from the normal, in this case 30 degrees.

In addition to ...
By: DragBag2000. on 03 Feb 10, 03:51:48
In addition to solving the equation in terms of theta, you can also use the pythagorean thereom to find h or w in terms of the other variable, take the derivative with respect to whichever variable you chose to solve for, and then use that to find the optimal height or width. From there you can apply pythagorean thereom again to find your other variable, and then you could calculate theta by taking the arctangent of your (w/h) values.

That rain gutter is ...
By: lilsamuraijoe. on 27 Jan 10, 04:07:25
That rain gutter is staring at me with devil eyes.

Search Engine Optimization Secrets
Posted by: vincentflanders

Video duration: 144 seconds
Global video hits: 35652

The three most important tips

Related: webpagesthatsuck, web, design, search, engine, optimization

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Google Marketer's Playbook: Optimization Strategies, Part 1
Posted by: GoogleBusiness

Video duration: 3414 seconds
Global video hits: 29860

Learn basic Google AdWords optimization strategies: account structure, ad text, and keywords.

Related: google, adwords, online, advertising, playbook, marketers, internet, keywords, ad, text, account, structure, optimization

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Optimization with Calculus 3
Posted by: khanacademy

Video duration: 1049 seconds
Global video hits: 17200

A wire of length 100 centimeters is cut into two pieces; one is bent to form a square, and the other is bent to form an equilateral triangle. Where should the cut be made if (a) the sum of the two areas is to be a minimum; (b) a maximum? (Allow the possibility of no cut.)

Related: calculus, optimization, derivative, maximum, minimum

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Latest comments made on this video:

"I can already ...
By: laram24. on 27 Jul 10, 19:41:55
"I can already sense" LOL

This math is shit ...
By: hmodywakid. on 02 Jul 10, 11:49:25
This math is shit come and study math in mother russia

@tnmr42 That's the ...
By: O0oSorousho0O. on 01 Jul 10, 12:52:53
@tnmr42 That's the easy part dude....

So when dy/dx only ...
By: jonolollmao. on 16 Jun 10, 21:51:21
So when dy/dx only gives the max or min point, the other point can be found by substituting the boundary as in this case 0cm or 100cm ?

Well, I don't ...
By: n1a1s1i1m. on 27 May 10, 17:49:42
Well, I don't always like the idea of cracking every equation my way. Kinda because we're not allowed calculators, kinda because the calculus you infused in my head tells me to directly differentiate. And so once again, Sal Man saves the day! :D

Oh wow haha yea my ...
By: standish250. on 12 May 10, 04:13:02
Oh wow haha yea my bad don't know what I was lookin at

@standish250 it's a ...
By: thejugglenaut91. on 12 May 10, 02:05:37
@standish250 it's a^2

You lost me at 6:31 ...
By: tnmr42. on 04 May 10, 02:06:24
You lost me at 6:31 Sorry man. Your other vids are great, this one's just too damn long.

The Max/Min comes ...
By: Utubemember3. on 15 Apr 10, 01:29:11
The Max/Min comes from the +/- sqrt(3). Plus give Min. - Gives Max.

I love how you work ...
By: madscirat. on 07 Apr 10, 00:51:49
I love how you work problems without preprep. It allows everyone to see your thought process, imperfections included. I have taken your lead and shown a few problems on my site, but Im not nearly brave enough to do it your way yet.

I might be wrong ...
By: standish250. on 08 Mar 10, 23:33:42
I might be wrong but doesn't the derivative of f (a)= (a^4)/16 become f ' (a) = 4(a^3)/16 which = (a^3)/4? He has a/8 which means he took the 3rd derivative [for a to have no exponents] but in reality that would be f ''' (a) = 3a/2 If I'm wrong please explain how because that would mean his entire problem from then on is off. Thanks!

(a^2*Sqrt3)/4 --> ...
By: zsozsokel. on 05 Mar 10, 19:57:34
(a^2*Sqrt3)/4 --> area of equilateral triangle where a is a side.

this video could've ...
By: ofarevolution441. on 22 Jan 10, 04:18:58
this video could've been like 6 minutes shorter if you just used pencil and paper and a camera. :p regardless, thanks for the help!

lol i cracked up ...
By: gobberpooper. on 20 Dec 09, 22:41:22
lol i cracked up when he goes "calculatooor!" and drags the calculator window over

The wire has to be ...
By: bkisme. on 08 Dec 09, 08:07:55
The wire has to be distributed across the entire square, therefore each side would be 25. 25^2 = 625 Sal was correct in his calculation of the area of the square.

thank you soo much. ...
By: ManUtdMU7. on 08 Dec 09, 04:17:36
thank you soo much...you are a lifesaver!

If the total length ...
By: chett16. on 06 Dec 09, 16:12:07
If the total length is 100 then each side is 25

This video has to ...
By: angry77561. on 06 Dec 09, 15:09:34
This video has to have some mistakes. We know that the area of a square is x^2 and that the length of the wire is 100. He should have gotten 1000 for the area of the square instead of 625.

thanks again :D
By: Xlaxsauce. on 22 Nov 09, 22:16:20
thanks again :D

(post continued -- ...
By: zoazoon. on 26 Sep 09, 09:33:49
(post continued -- I'm discussing a problem a commentor brought up, not the one in the video) If we can show that theta is maximized when x = 2, we will have proven what we intended to prove. Theta is alpha + beta which is arctan(a/(bx))+ arctan(a/b -(a/(bx))). Use scaling to turn a/b into another constant, k. Then differentiate and find that the only critical point is x = 2. Checking all possible extrema confirms that x = 2 is indeed an absolute maximum for theta.

Cool problem ...
By: zoazoon. on 26 Sep 09, 09:18:08
Cool problem rryking! I solved it after a couple hours of deep thought. Let A be the height of the painting, B the distance between the observer and the painting, alpha the angle between the bottom of the painting and the observer's line of sight, beta the angle between the top of the painting and the line of sight. Finally, the vertical distance from the bottom of the painting to the point where the line of sight hits the wall is a/x, so that the rest of the painting's height is a - a/x

I did it in a very ...
By: fiza200555. on 31 Aug 09, 21:11:24
I did it in a very simplified way, for square with side S, perimeter 4S=l, n for the triangle with side t, perimeter, 3t=100-l, now we getthe sum of areas as S^2+t^2*root3/4.substitute for S and t in terms of l and solve. I hope it was clear enough

I think it means ...
By: sharvil1993. on 17 Aug 09, 07:53:10
I think it means that after the 1st cut, there should be no more cuts in making the square and triangle.

UUUGGghhhhhh I have ...
By: Zanirtak. on 19 May 09, 01:33:04
UUUGGghhhhhh I have a similar question but the answer I'm getting is 32 and the total length of the wire is 14.........

It wants u to find ...
By: irlazybum. on 14 May 09, 01:42:16
It wants u to find the min and max of the two combined areas from square and the triangle. so u'd have to find 2 crit values. but if in the problem there came to be 1 critical point (like it this in this problem, 1 crit point at 56.6) u would have to check the end points (like EVT) to see if there are bigger values than that of the crit point . that's why it said allow the possibility of no cut, so u would have to check when the rope is used for only for the area of the triangle or square

Optimization with Calculus 2
Posted by: khanacademy

Video duration: 716 seconds
Global video hits: 21842

Find the volume of the largest open box that can be made from a piece of cardboard 24 inches square by cutting equal squares from the corners and turning up the sides.

Related: calculus, optimization, derivative, maximum

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Latest comments made on this video:

You are amazing, I ...
By: RedScorpion97. on 17 Jul 10, 19:26:01
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You Sir, are my ...
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WE ALL LOVE YOU!!!
By: chickencombo3. on 16 May 10, 23:11:00
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i LOVE your little ...
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i LOVE your little side comments in your videos; they always make me smile. thank you for these videos! my professor is extremely boring with his lectures, but you make calc fun. you're awesome!

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thank for this vido ...
By: dianelly. on 29 Apr 10, 19:20:32
thank for this vido, GOD bless u

hey how old are you ...
By: ohlalaxobeer. on 23 Apr 10, 01:39:28
hey how old are you are you a professor? or a student you seem smart

i should have ...
By: vivian333999. on 05 Apr 10, 04:41:14
i should have memorized my times tables up to 25... hahah. u r a genius

@daseiner lol thats ...
By: misscollegiate08. on 30 Mar 10, 17:27:57
@daseiner lol thats alright :)

@misscollegiate08 ...
By: daseiner. on 25 Mar 10, 18:08:01
@misscollegiate08 You're absolutely right. Bad day, sorry for any confusion.

@daseiner it is x = ...
By: misscollegiate08. on 25 Mar 10, 16:27:07
@daseiner it is x = 4

its six bro...
By: imadElghourani. on 23 Mar 10, 22:56:26
its six bro...

Bless you, calculus ...
By: OARHEGOS. on 15 Mar 10, 22:15:39
Bless you, calculus is hard, but listening to you is fun. Thanks.

The great Sal does ...
By: righteousgroove. on 12 Mar 10, 23:00:45
The great Sal does not need a calculator :P

8:49 to 8:53 LOL!!! ...
By: TigerXC26. on 01 Feb 10, 06:38:11
8:49 to 8:53 LOL!!! i go thru da pain like u do hahahaha!! a calculator would help u know..

like one time ...
By: hockeymo. on 20 Jan 10, 04:22:27
like one time during calculus class, i forgot 2x3.

you are my hero!
By: sharron2792. on 11 Jan 10, 09:23:56
you are my hero!

@shaneymane or RPI ...
By: DrPeppable. on 18 Dec 09, 22:09:45
@shaneymane or RPI please =)

@riku0228 no, they ...
By: DrPeppable. on 18 Dec 09, 22:07:33
@riku0228 no, they have to multiply to 48, 8*8 = 64

Search Engine Optimization and Blogs
Posted by: internetmoguling

Video duration: 604 seconds
Global video hits: 30474

Great 10 minute lesson on SEO and Blog Marketing. Check out my new Twitter Web App for Twitter Marketing. It has built in SEO www.fol.la

Related: seo, tips, search, engine, optimization, optimisation, free, blogs, blog, marketing, web, site, submission

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Blogs do play a ...
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Search Engine Optimization SEO Tutorial - Google allinanchor
Posted by: mixer28

Video duration: 87 seconds
Global video hits: 15855

www.gsinc.co.uk Discover Google's all in anchor command and see how you can use this useful research tool yourself. Search Engine Optimization SEO Video Tutorial by Gareth Davies of GSINC Ltd. For more SEO, Link Building and ECommerce tips visit www.gsinc.co.uk

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Sacramento Search Engine Optimization SEO
Posted by: juliemarg

Video duration: 62 seconds
Global video hits: 216

Get on the Map getonthemap.us Local Search Engine Optimization, Social Media Coaching & Consulting, Reputation Management and Video Marketing for small businesses in Northern California and Northern Nevada. Locall owned & operated in Sacramento CA. CEO Julie Gallaher.

Related: seo, local search, sacramento, search engine optimization

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