- #1

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## Homework Statement

A piece of cardboard is 14 inches by 10 inches and you are going to cut out the corners and fold up the sides to form an open box. Determine the height of the box that will give a maximum volume.

## Homework Equations

V = lwh

## The Attempt at a Solution

Using

(10-2x) as l

(14-2x) as w

and x as the height:

V = (10-2x)(14-2x)x = 4x^3 - 48^2 +140x

dv/dx = 12x^2 - 96x + 140

0 = 12x^2 - 96x +140

x = 6.08, 1.92 or 1/3(12±√39)

.... this is where I get lost. I feel like I messed it up somewhere because I get weird numbers for x. Technically, the 6.08 number is impossible, so x would have to equal 1.92. But still, I feel uncomfortable with these numbers.