What is the maximum possible product that can be attained by two numbers with a sum of −8?

For this case, the first thing we must do is define variables:
 x = y = unknown numbers.
 We have the sum of the numbers is -8:
 
 The product of the numbers is:
 
 We write the product based on a variable:
 
 Rewriting:
 
 We derive the function:
 
 We match zero:
 
 From here, we clear the value of x:
 
 Then, the maximum product is:
 
 
 The maximum product is given by:
 P = 16