# Question #e05e2

##### 2 Answers

#### Explanation:

Lets arrange pairs of numbers which add to

We notice that as the numbers get closer, the difference between them gets less, but their product increases.

The smallest difference will be when the two numbers are equal and their product will therefore be the biggest.

The numbers are

#### Explanation:

Let one number be

Then, the other number is

Let the product of the numbers be

So,

Differentiating with respect to

The critical value is when

Let's make a variation chart

There is a maximum at

We confirm this by calculating the second derivative

As