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