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Let \(x\) and \(y\) be real numbers such that \(0 \le x \le 1\) and \(0 \le y \le 1.\) Find the maximum value of \(x^2 y - xy^2\).

 

 

any tips / hints / solutions would be greatly appreciated! :)

 Feb 4, 2021
 #1
avatar+73 
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the answer was \(1 \over 4\)!

 

to anyone who has also been trying to tackle this problem: 

 

you could factor the expression like so:

 

\(xy(x-y)\)

 

then, since you are trying to find the maximum value, you can assume that \(x \ge y\). by AM-GM, \(y(x - y) \le \frac{x^2}{4}\), and then continue from there:)

 Feb 4, 2021

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