Calculus

An open box is to be made from 8 inches by 18 inches piece of cardboard by cutting
squares of equal size from the four corners and bending up the sides. How long should
the sides of the squares be to obtain a box with the largest volume?

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  1. If the squares have side x, then the volume is
    v = x(8-2x)(18-2x) = 4x^3 - 52x^2 + 144x
    dv/dx = 12x^2-104x+144 = 4(3x^2-26x+36)
    so find where dv/dx = 0 and make sure that is a maximum, not a minimum.

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    oobleck
  2. worksheet 4 yan ha, send answers naman dyan

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