# Calculus

An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides, find the dimensions of the largest box that can be made in this way.

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1. if the squares are of side x, then

v = x(12-2x)^2 = 4x^3-48x^2+144x
dv/dx = 12x^2 - 96x + 144
= 12(x-2)(x-6)

so, v has a max at x=2.

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2. Thank you sir.

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3. A piece of cardboard measuring 13 inches by 11 inches is formed into an open-top box by cutting squares with
side length x from each corner and folding up the sides.

a. Find a formula for the volume of the box in terms of x

b. Find the value for x that will maximize the volume of the box. Round to 2 decimal places if needed.

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4. v=(13-2x)(11-2x).x

dV/dx= 3x^2-96x+143

use Q formula x= (-b +or - (b^2-4ac)^1/2)/2a

ans x=2.26

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5. v=(13-2x)(11-2x).x

dV/dx= 3x^2-96x+143

use Q formula x= (-b +or - (b^2-4ac)^1/2)/2a

ans x=1.98

sorry for the previous ans

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