Maximum Volume of an Open Top Box

[Carl_M]

Homework Statement

Is there another way to do this question?
Is this right?

L = 50-2x
W = 40-2x
Height= X

Homework Equations

//

V=L x W x H
V= (50-2x)(40-2x)(x)
V= (2000 -180x +4x²)(x)
V= 2000x -180x² +4x³
V= 4x³ - 180x² +2000x
V' = 12x² -360x +2000
X = (360 (+/-)sqrt(360²-4(12)(2000))) / 2(12)
X = 7.36...

How would I do this without using f ' ( x ) ? nor graph it

The Attempt at a Solution

 

[numberjuan412]

Are they asking you to do it without taking the derivative and setting it equal to zero?
Graphing is never necessary. Just for convenience.

 

[Carl_M]

No, but how would I do that?

It's not required or anything nor is it asked.