from a cardboard box 12 in by 8 inches are cut out so the sides can be folded up to make a box . What dimentions will yield a maximum volume? What is maximum volume?

Question

we got our V = 4x^3--40x^2+96x
V'=12x^2-80x +96
then we know to use quadratic equation
I get 20( +/-) sqrt 112/6
this is where stuck please help thanks

Answer 1

you have two answers. One will be greater than 8, so it is useless. So, use

(10-2√7)/3 = 1.57
max v = 64(10+7√7)/27

Answer 2

the quadratic solutions are relative max/min points on the graph (you obviously want the max)

test the solutions in the original equation

x < 4 because of the 8 in side