Squares of side length x are removed from the 4 corners of an 11in by 8.5in piece of paper. The sides are then folded up to create an open-top box. Write a funcion that determines the volume of the box and determine the functions range. How much should be cut from the corners to determine the box's maximum volume?

1 answer

make a sketch to see that

V = x(11-2x)(8.5 - 2x)
= x(93.5 - 39x - 4x^2)
= 93.5x - 39x^2 - 4x^3
dV/dx = 93.5 - 78x - 12x^2
= 0 for a max of V

solve for x