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