Math

A rectangular piece of cardboard measuring 12 cm by 18 cm is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each square in centimetres.
a. Give the restrictions on x.
b. For what value of x will the volume be a maximum?

My answer:
a. 0<x<6

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  1. a. correct
    b. The volume with the cuts made and the sides folded up is

    v = (12-2x)(18-2x)x = 4x^3-60x^2+216x

    If you have calculus, then
    dv/dx = 12(x^2-10x+18)
    dv/dx=0 when x=5-√7 ≈ 2.35

    If no calculus, then a graphical or numeric method is needed.

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