Find two nonnegatives number whose sum is 9 so that the product of one number and square of other number is a maximum 10.

Answer 1

Previous answer is wrong! Checkout the graph of his two functions:

https://www.desmos.com/calculator/ws0oobhabg

The answer is the union of two open intervals:

(0, 4-srqt(15)) and (4+sqrt(15), 9).

Solved correctly, you get a cubic equation that can be factored as follows:

(x - 10) (x - 4 - sqrt(15)) (x - 4 + sqrt(15))

Answer 2

x+y=9

xy^2 = x(9-x) = 9x - x^2 = f(x)

f'(x) = 9 - 2x

0 = 9 - 2x

2x = 9

x = 9/2

y = 9 - 9/2 = 9/2

x=y=9/2