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Maximum Volume of a box

  • Thread starter zeezey
  • Start date
  • #1
11
0

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
 

Answers and Replies

  • #2
eumyang
Homework Helper
1,347
10
First off, you didn't round to the nearest tenth. :wink:

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)?
 
  • #3
11
0
What am I supposed to get if I plug those numbers in to that equation? Those points are valid if I plug them into the derivative equation I found. Is my derivative wrong ?
 
  • #4
eumyang
Homework Helper
1,347
10
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.
 

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