Pre Calculus

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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  1. L = 13 - 2x
    w = 11 - 2x

    V = (13-2x)(11-2x)x

    V = (143 - 48 x + 4 x^2)x

    V = 4 x^3 -48 x^2+143 x
    find where dV/dx = 0

    0 = 12 x^2 - 96 x + 143

    x = [ 96 +/- sqrt(9216-6864)]/24

    x = [96 +/- 48.5 ]/24

    x = 1.98 in
    or
    x = 6.02 (too big, no width left)

    so about 2 inches high

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