Can you answer this problem for 10 points
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Can you answer this problem for 10 points

[From: ] [author: ] [Date: 11-10-21] [Hit: ]
A certain airline requires that the total outside dimensions (length + width + height) of a carry-on bag not exceed 37 inches. Suppose you want to carry on a bag whose length is twice its height. What is the largest volume bag of this shape that you can carry on a flight? (Round your answer to the nearest integer.)-So the dimensions of the bag are going to be x by 2x by 37 - 3x.To find the extreme points,......
i cant figure this last problem out, i would really appreciate the help,

A certain airline requires that the total outside dimensions (length + width + height) of a carry-on bag not exceed 37 inches. Suppose you want to carry on a bag whose length is twice its height. What is the largest volume bag of this shape that you can carry on a flight? (Round your answer to the nearest integer.)

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So the dimensions of the bag are going to be x by 2x by 37 - 3x.

The volume of this bag is V = 2x^2 (37 - 3x) = 74 x^2 - 6x^3

dV/dx = 148x - 18x^2

To find the extreme points, we must solve dV/dx = 0

148x - 18x^2 = 0
2x(74 - 9x) = 0
x = 0 or x = 74/9

So the largest volume is

148(74/9) - 18 (74/9)^2 = 405224/243 ≈ 1668 in^3
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