+132 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! :)
+132 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:)
