SOLUTION: An open box is made from a rectangular piece of material, 13 inches by 10.5 inches, by cutting equal squares (let it's side is x)from each corner and turning up the side. 1. Wha

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Question 1061339: An open box is made from a rectangular piece of material, 13 inches by 10.5 inches, by cutting equal squares (let it's side is x)from each corner and turning up the side.
1. What is the dimensions of the box that has the maximum volume (V max)
2. What is the maximum volume of the box (V max)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the edge length of each square to be cut.

v for volume, will be
highlight%28v=x%2813-2x%29%2810.5-2x%29%29

v=4x%5E3-47x%5E2%2B136.5x

Maximize v, by looking for local max value or values.
dv%2Fdt=highlight_green%2812x%5E2-94x%2B136.5=0%29

x=%2894%2B-+sqrt%282284%29%29%2F%282%2A12%29

highlight_green%28x=%2847%2B-+sqrt%28571%29%29%2F12%29
Two values to examine. Which of them is a maximum?
Will it work with the dimensions of the sheet that you are given?

The decimal approximations for those values to examine are 1.93 and 5.91.
If you think about the basic shape to expect for a cubic equation, such as for your volume,
the maximum value will be to the left of the minimum value for the volume function.
Expect x=1.93 to be your answer.