Challenging math problem.

Determine the regions of the pq-plane for which the function f(x,y) = 2px + qy^2 restricted to the curve x^3 + y^3 = 1 has exactly one and exactly three critical points, respectively.

If the critical point is (x,y), what is x+y?

Hope you enjoy this problem!

No one I know, knows how to solve this question. If you can solve it please give your solution step by step!

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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Comments

pq-plane ?

Ahmed Taha - 8 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$