Optimization: sum of squares | Applications of derivatives | AP Calculus AB | Khan Academy

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What is the minimum possible value of x^2+y^2 given that their product has to be fixed at xy = -16. Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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X^2=16 ==> x=4 or -4. så why didn`t you talk about the situation when x=-4? plz

decojosephson

In hindsight, x and y both having an absolute value of 4 makes sense because this question is basically asking you to minimize the diagonal of a rectangle of constant area. You can try out a few rectangles and you quickly find that a square is the best shape.

DanielSan

Is it true to say that x = -4 and y = 4 is the answer as well? I tried to draw out the graph and it actually has two minima, at x = 4 and -4

kahhuanyap

B= -.5 C= 2.5
First you take derivative
y'=3x^2 +2bx, evaluate at (1, 2)
b=-.5
so equation is y=x^3 +(-.5)x^2+c evaluate at (1, 2)
c=2.5
...I'm kinda of questioning that though, but hopefully its right

AlphaNumeric

Shouldn't it be x^-2 at the end of c(x)?

JamesTsividis

Thanks for the good work. :)
BTW didn't you forget to divide the area of the triangle by 2?

PiEndsWith

hi men can you find (b, c) in this function y=x^3+bx^2+c
if tangent m=0 for this point is (1, 2) ?

hamamath

Ya i thought so but posted anyways. Did you figure it out? I'm curious.

AlphaNumeric

Ah yeah I figured... realized after I did my work. Did you find the answer, its a kind of interesting problem

AlphaNumeric

Optimization: sum of squares | Applications of derivatives | AP Calculus AB | Khan Academy

Optimization: sum of squares | Applications of derivatives | AP Calculus AB | Khan Academy

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