Question

Help I dont understand how to solve!!!

You construct an open top box by cutting equal sized squared (x by x) in each of the 4 corners of a 14 inch by 24 inch sheet of paper and then folding up the sides. Find a function for the volume of the box as a function of x and determine the largest volume possible.

Answer 1

V = L * W * H

Width is 14 but if you cut off x from the top and the bottom you have
W = 14 - 2X

LEngth is 24 but if you cut off x from the left and the right you have
L = 24 - 2X

Height is X how much you cut off so you can fold it up
H = X

V = (14 - 2X)(24 - 2X)X
V = (336 - 28X - 48X + 4X^2)X
V = X(4X^2 - 76X + 336)
V = 4X^3 - 76X^2 + 336X

Can you use a graphing calculator and see at which x value does the graph have its maximum point.

Answer 2

Thanks I had gotten that far and I just didnt know where they were getting the max from!