Question

Find the two positive numbers whose sum is 110 and whose product is a maximum.

Answer 1

A maximum of what?

Answer 2

y + x = 110 = maximum

Answer 3

:)

Answer 4

x+y=110; xy=M
xy is what you wanna maximize.
Solve the first for y
y=110-x
Plug in your max.
(110-x)(x)=M
110x-x^2=M
Differentiate:
110-2x=dM/dx
Set equal to zero.
110-2x=0
2x=110
x=55
Try pluggin in x=54 and x=56 to make sure that it is a max (First derivative test)