Optimization Problem #4 - Max Area Enclosed by Rectangular Fence

[chewedtoothpicks]

I'm confused. See in my mind logically max area of a perimeter of 500 would be 500/4 sides = 125. Being that in reality the closer you are to a square will provide you with the maximum possible area. So with that, since 500 is a nice number, 125+125+125+125 for all sides = 500. So L x W = 125 x 125 = 15,625sq ft. Which is half of what you got for your area. If I did 125 x 250 yeah then I'd get 31,250. But that would mean L=250 W=125. 250x2 + 125x2 = 250. Then our total perimeter is 750. help me?

[chewedtoothpicks]

@chewedtoothpicks oops, i meant: L=250 W=125. (250x2 = 500) + (125x2 = 250) = 750

[ImJustAbi]

@chewedtoothpicks It's only 3 sides not 4, 2 widths and 1 length or vica versa. The river is the 4th side.

[chewedtoothpicks]

@ImJustAbi Aha! How did I miss that lol, thank you. :D

[nanone1994]

oh what an amazing teacher you are !! thanks alot <3 you know at the beginnig of this school year i hated derivaitives to death but when i discovered your videos and whatched them all guess what I SCORED 100 out of 100 in my first semester final exam!! this is a great achievement for a senior girl like me! :) thanks alot Mr.Patrick .....

[patrickJMT]

@nanone1994 congrats on your great score :)

[wenndy1994]

Okay so If they do ask for dimensions is their like an extra step to do so because I have this problem (except it used 200 ft. And has two adjacent rectangles) but I don't know how to find the maximum area of dimensions .

[iProjectMobius]

Ha ha! Our teacher used this problem as an example in class! That means a problem like this will probably be on the test...

[janialopez4242]

I had the same question on my past test... i also wish i had watch this :( but this is good review

[acaveman03]

exact problem i had on a test a month ago... i wished i had watched this before hand

[LadyMacbeth22]

could you write a perimeter equation as the constraint in this problem?

[djerock72192]

Can I just borrow your brain for my calc final tomorrow?? ;-P

[patrickJMT]

@djerock72192 no, i will be using it

[T3N0RI0]

this was on my test and is the only video i did not watch about optimizations -_-'

[darkwolf811]

seeing the rectangle visually really helped me. thanks. Also, have you ever heard of completing the square to convert the function to vertex form?

[patrickJMT]

@darkwolf811 yep

[ICarnag3I]

Please do one with profit maximization (Economics).

[ewgross1294]

you're my hero. 

[Smirnov25]

Extremely concise, especially concerning the 2 unknown sides and relating both to the total, instead of saying the length or side opposite to the river were "y". That was a really good idea.

[elsalfo]

I did this by myself after watching you do problems # 1 and 2. I LOVE YOU!

[AceAites]

I'm pretty sure most farmers wouldn't be able to even do this type of problem. LOL. EXCELLENT VIDEO.

Btw, why would you want to find A(x) where it is undefined ? That part confused me. :P

[theultimategirl26]

@AceAites He was just pointing out that when you do this problem when it is not dealing with a rectangle or some area, that usually you find where A(x) is undefined. But he didn't because we don't have an undefined area!! :D

[ant6762]

can you not just use -b/2a to calculate the vertex of the parabola?????

[patrickJMT]

@ant6762 yep!!!!!!

[glitchnoise]

I like how you started off like you were teaching a little kid about cows being unable to swim and then BAM, start talking about functions and derivatives.

[PhillipBroussard]

So... That problem took 10 minutes and I have 20 problems like that on my exam. Is it just me or does that equal over 3 hours of test taking?

[elsalfo]

@PhillipBroussard

Took me like 2 minutes and it's the first one I've done. He's teaching so he goes way slower than necessary for clarity.

[normandie350]

this is the first time i learn pen means something other than a writing instrument =|

[koopa322]

Lol we solve this question using the quadratic equation.

[IEGSmath]

Thanks for this one Patrick! it is a typical type of optimization problem on our Math C National tests here in Sweden - can't wait to share with our students. Yep ... this one is added to the Math C playlist.

[TeeEye84Plus]

I hope we get an easy one like this on our exam

[aabhas11111]

The Way I was taught to do this was... by taking a double derivative.... in order to ensure if it actually maximizes or minimizes the function... can you trow some light on that ?

[AsianSpaghetti]

Hi I'm in high school and when my teacher surprised me with the joy of functions; I struggled... Can you please help me understand the topic because I really have no idea what I'm doing... P.S I'm really serious about what I'm saying.

[Jaquis198]

i'm not too sure, but i think this exact problem was on one of my honors precalculus tests last year lol awesome

[monkeydemon109]

When I was in calculus I spent 10 weeks (the length of the quarter) trying to get this down.... and my professor barely helped me at all. You just made it ridiculously clear in under 10 min.

[dhcrazy333]

Took the BC Calc AP test today. Wasn't too bad. Though there was a Taylor series problem that I knew how to do the first half, but I would REALLY like you to explain how to do the 2nd half. Too bad I have to "wait 48 hours" before I can discuss the nature of the problem :)

[lolzgunner101]

@dhcrazy333 was that problem the last frq problem cause yeah, that problem stumped me, especially 6 d

[dhcrazy333]

@lolzgunner101 It was the last free response non calculator question, so I guess yeah, it was question 6. I had no idea how to do D or C. I got A and B no problem, but the second half, I would REALLY like Patrick to explain.

[CaNaDiiAnBaCoN]

Patrick, why are you doing all of the questions that were on my calculus test that was last week, now......

[patrickJMT]

@CaNaDiiAnBaCoN sorry, i only had 990+ videos up for you last week.

[CaNaDiiAnBaCoN]

@patrickJMT haha, im kidding, just this is the exact problem that was on my test except 800 instead of 500.

[patrickJMT]

@CaNaDiiAnBaCoN : )