SOLUTION: What is the maximum volume of a open box created from a square of side length 24? Keep in mind that V=LWH. So for this problem the dimensions are as follows:
L = 24-2x, W = 24-2x
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L = 24-2x, W = 24-2x
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Question 664592: What is the maximum volume of a open box created from a square of side length 24? Keep in mind that V=LWH. So for this problem the dimensions are as follows:
L = 24-2x, W = 24-2x and H = x. The maximum volume will be where the volume equation is the greatest.
You are to determine:
1. The volume equation.
2. The maximum volume.
3. The value of x that maximizes the volume.
Explain each step. Answer by solver91311(24713) (Show Source):
Set the first derivative equal to zero and solve. This is a quadratic so you will get two roots, each of which represents the abscissa of a local extremum of the original function.
Take the second derivative:
Evaluate
where is either of the abscissas of the possible extreme points. If then is the abscissa of a local maximum, if then is the abscissa of a local minimum. If , the second derivative test is inconclusive, but it is a possible inflection point. In the latter case, for this problem, calculate the volume for the value of in question and see if it makes sense as a possible value that could give a maximum volume.
John
My calculator said it, I believe it, that settles it
