# How do you find the two positive real numbers whose sum is 40 and whose product is a maximum?

##### 1 Answer

You have to find first a function to represent the problem stated, and then find a maximum of that function

#### Explanation:

The problem states that we are looking for two numbers

We would like to find where the product

So we now have a one-variable function

To do that we calculate the derivative

Now the second derivative

But we also know that

The solution is then