Find two integers whose sum is 160 160 and whose product is as large as possible.

Answer 1

Let x and y be the integers

x+y=160

y = 160-x

Product:

p(x) = xy = 160x-x²

p'(x) = 160-2x

160-2x=0 ===> x= 80

y = 160-80 = 80

p"(x) = -2 <0 so is a maximum at p(80) by second derivative test