This questions english is hard not the math.

Awsom Guy · #1 $Old$ November 8th, 2009, 12:20 AM

Hi
This is my question.
The sum of two numbers is 30. If one of them is x, write down an expression for the product of one number and the square of the other. Find the numbers if this product is to be maximum.

Can someone show me how to do this or start this thanks.

Prove It · #2 $Old$ November 8th, 2009, 01:06 AM

Quote:

Originally Posted by Awsom Guy $View Post$

Hi
This is my question.
The sum of two numbers is 30. If one of them is x, write down an expression for the product of one number and the square of the other. Find the numbers if this product is to be maximum.

Can someone show me how to do this or start this thanks.

The sum of two numbers is 30.

Call these numbers $x$ and $y$ .

Then $x + y = 30$ .

It is important to note that $y = 30 - x$ .

The product of one number $x$ and the square of the other $y^2$ is obviously $xy^2$ , which you can write as $x(30 - x)^2$ .

You want this product to be a maximum.

So $f(x) = x(30 - x)^2$ .

Find the derivative, set it equal to 0, solve for $x$ , then use $x$ to find $y$ .