Question

a box with no top is to be made out of a 6' by 10' piece of cardboard with x' squares cut out of the corners. The sides will be folded up to make the box. Find the value of x that maximizes the box

Answer 1

1.21'

Explanation:

Volume = (6-2x)(10-2x)(x)

= (60-12x-20x+4x²)(x)

= 4x³-32x²+60x

dV/dx = 12x² - 64x + 60 = 0

3x² - 16x + 15 = 0

x = 4.1196 , 1.2137

d²V/dx² = 6x - 16

at x = 4.1196, +ve

at x = 1.2136, -ve

x should be small for max volume,

So x = 1.21' (3 sf)