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3.6 Mathematical Models: Constructing Functions

3.6 Mathematical Models: Constructing Functions. An open box with a square base is to be made from a square piece of cardboard 30 inches wide on a side by cutting out a square from each corner and turning up the sides.

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3.6 Mathematical Models: Constructing Functions

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  1. 3.6Mathematical Models: Constructing Functions

  2. An open box with a square base is to be made from a square piece of cardboard 30 inches wide on a side by cutting out a square from each corner and turning up the sides. (A) Express the volume V of the box as a function of the length x of the side of the square cut from each corner.

  3. Volume = (length)(width)(height) (B) Graph V=V(x).

  4. (C) For what value of x is V largest? V is largest (2000 cubic inches), when x = 5 inches.

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