Optimization, a box with an open top, given volume, find the minimum surface area

[@rohanraj-sv8tb]

thanku very much you make this question very easy....good explanation👍👍

[@enthusia492]

God, I remember having this question on a Final for Calc1 Applications. Still gives me nightmares!

[@gammano0b858]

I ust cancelled the x^2 on the bottom by multiplying it on both sides to get to 2x^3 - 128000 = 0, because x can't be zero in this case (not a solution), and then dividing by 2 and noticing that 64000 = 64 * 1000 which is the product of two cubes, namely 4 and 10, thus the answer is 40

[@TheIvar19]

at 4:40 why the hell would you solve it that way

[@intuitiveclass6401]

i was shocked as well, only thing i can think of is that it helps when checking values to see if there is truly a min/max lol

[@joshuayoo1306]

But if he had added 128000/x² tot he other side, he would have gotten the right answer within 3 seconds. His method took over 10 seconds. In the ap test, time is literally money, since you paid to potentially save hundreds on another college class

[@danielkovacs6809]

Hi! I just found a constant (approximately 2,2911249) by adding up "infinitely times" iterated heights beginning in a 60-60-60 degree triangle, then iterating it in 30-60-90 degree triangles so that the height lines were perpendicular to the hypotenuses (and in the end I found a point that these lines were approaching). The question is the following: does this number already exist, and if yes, then how is it called? Sorry, if my explanation was kind of messed up, but I'm not that good at english. Thanks for the answers in advance. :)

[@田村博志-z8y]

Let x^2*y = a^3 be fixed. We consider the minimum of x^2 + 4xy. We note that x^2 + 4xy = x^2 + 4x( a^3/x^2 ), = x^2 + 4a^3/x, = x^2 + 2a^3/x + 2a^3/x. By AM-GM inequality we have ( x^2*2a^3/x*2a^3/x )^( 1/3 )

[@gjoe3756]

Now do something with multivariable and use partial derivative

[@ILoveMaths07]

You look so good with hair!

[@prakharjain21]

Are these from The Archives or are you aging backwards nowadays

[@siddharthamondal4346]

meow