Question

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

Answer 1

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:
 $x + y = -8$
 The product of the numbers is:
 $P = x * y$
 We write the product based on a variable:
 $P = x * (- 8 - x)$
 Rewriting:
 $P = -8x - x ^ 2$
 We derive the function:
 $P '= -8 - 2x$
 We match zero:
 $-8 - 2x = 0$
 From here, we clear the value of x:
 $2x = -8 x = -8/2 x = -4$
 Then, the maximum product is:
 $P = -8 * (- 4) - (-4) ^ 2 P = 16$
 Answer:
 The maximum product is given by:
 P = 16