# How do you find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other number is a maximum?

##### 1 Answer

Feb 27, 2015

Let's call the first number

Then the other will be

So the question translates to:

Find the maximum of

The maximum is when the derivative is set to

And the other number will be

Check the answer:

To be sure that this is a maximum you could check for: