# What are two positive numbers whose sum of the first number squared and the second number is 54 and the product is a maximum?

##### 1 Answer

May 9, 2018

#### Explanation:

Let the numbers be

#x^2 + w = 54#

We want to find

#P = wx#

We can rearrange the original equation to be

#P = (54 - x^2)x#

#P = 54x - x^3#

Now take the derivative with respect to

#P' = 54 - 3x^2#

Let

#0 = 54 - 3x^2#

#3x^2 =54#

#x =+-sqrt(18) =+- 3sqrt(2)#

But since we're given that the numbers have to be positive, we can only accept

At

At

Therefore,

Hopefully this helps!