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# algebra

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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

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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