Question 586732
The sum of two nonnegative numbers is 9. Find these two numbers
knowing that the product of one number and the square of the other number
is a maximum.
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P = x^2*(9-x) = 9x^2-x^3
{{{f(x) = -x^3 + 9x^2 - P}}}
f'(x) = {{{-3x^2 + 18x = 0}}}
-x*(x-6) = 0
--> x = 0, x = 6
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@ x=6, max value = 3*6^2 = 108