A piece of cardboard measuring 14 inches by 8 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides.

Question

FIND:
1). a formula for the volume of the box in terms of x
2). the value for x that will maximize the volume of the box

Answer 1

v = (14-2x)(8-2x)x = 4(x^3-11x^2+28x)
dv/dx = 4(3x^2-22x+28)
so, where is dv/dx = 0 ?