L = 18-2x
w = 18-2x
h = x
V = x(18-2x)^2
dV/dx = 0 for max or min
0 = x (2)(18-2x)(-2) + 1 (18-2x)^2
0 = -4x (18-2x) + 324 - 72 x + 4 x^2
0 = -72 x + 8 x^2 + 324 -72 x + 4 x^2
0 = 12 x^2 - 144 x + 324
0 = x^2 - 12 x + 27
0 = (x-3)(x-9)
x = 3 or 9
but 9 will not work (is V=0) so use 3
A square sheet of cardboard has sides 18cm. Four equal portions are cut away from the corner and discard. The sides are then twiced up to form a restangular box. What are the dimension of the box formed that will have max volume?
1 answer