Find two numbers whose difference is 124 and whose product is a minimum. (smaller number) (larger number)

For this case, the first thing we must do is define variables.

We have then:

x: unknown number 1

y: unknown number 2

The difference of both numbers is 124:

The product of both numbers is:

Writing the product based on a variable we have:

Rewriting:

To find the minimum of the function, we must derive:

We equal zero and clear x:

Then, the value of the other number is given by:

The searched numbers that meet both conditions are:

smaller number = 62

larger number = -62