Question

what is the maximum product of two numbers whose sum is -4?

Answer 1

x+y =-4
x=-y - 4 = -(y+4)

x y = -(y+4) y

use x = 0 , y=-4 and get 0 as product, which is maximum not negative.

Doesn't limit the absolute value of the product significantly, could be infinite

Answer 2

If the two numbers are x and y, I think the answer is x = -2 and y = -2.
Normally a square shape maximizes area. It's a common type of question.

x + y = -4
We want to know for x times y, what is the maximum?
x = (-y -4) from above.
xy becomes (-y-4)(y)= -y^2 - 4y
Do you know how to do derivatives yet?

Answer 3

4 times 0 is 0
(-2)(-2) = 4

Answer 4

I think @jam133 is right and I am wrong. Sorry.

Answer 5

It is a tricky question!