A long rectangle sheet of metal, 15 inches wide is to be made into a rain gutter by turning up equal amounts on each side so that they are perpendicular to the sheet. How many inches should be turned up in order to give the gutter its greatest capacity (i.e. maximize the costal-sectional area).

Answer 1

height = x
width = (15-2x)

A = x(15-2x) = 15 x - 2 x^2
at max or min dA/dx = 0
= 15 - 4 x
so
x = 15/4 (wish they had given us 16 :)