Maximum Volume of a Box: How to Optimize Cardboard Usage for Chocolate Boxes

[zeezey]

Homework Statement

Chocolate Box Company is going to make open-topped boxes out of 5 × 14-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way? (Round your answer to the nearest tenth.)

Homework Equations

V = length * width * height

The Attempt at a Solution

V(x) = x(14-2x)(5-2x)
=70x-38x^2+4x^3

d/vx = 12x^2 - 76x + 70
12x^2 - 76x +70 = 0
= 1.11 and 5.21

 

[eumyang]

First off, you didn't round to the nearest tenth.

Second, are you sure that both answers are valid? What happens if you plug in those values for x in
V(x) = x(14-2x)(5-2x)?

 

[zeezey]

What am I supposed to get if I plug those numbers into that equation? Those points are valid if I plug them into the derivative equation I found. Is my derivative wrong ?

 

[eumyang]

Your answers are not wrong, but not all answers may be valid. So you tell us: find V(1.11) and V(5.21), and note their signs.