What is the maximum product of two numbers whose sum isminus−44? what numbers yield this product?

Let the the numbers be x and y:
x+y=-44
thus
y=-44-x
thus the product of the numbers will be:
P(x)=x(-44-x)
P(x)=-44x-x^2
For maximum product P'(x)=0
from P(x),
P'(x)=-44-2x=0
solving for x we get:
-44=2x
thus
x=-22
thus the value of y will be : y=-44--22=-22
hence the answer is:
The numbers that yield maximum product is -22 and -22

Add up all the sides