Constructing a box From a rectangular piece of cardboard having dimensions 20 inches ×30 i...

Constructing a box From a rectangular piece of cardboard having dimensions 20 inches ×30 inches, an open box is to be made by cutting out identical squares of area x2 from each corner and turning up the sides (see Exercise).

Constructing a box From a rectangular piece of cardboard having dimensions 20 inches × 30 inches, an open box is to be made by cutting out an identical square of area x2 from each corner and turning up the sides (see the figure). Express the volume V of the box as a function of x.

EXERCISE

(a) Show that the volume of the box is given by the function V(x)=x(20 −2x)(30 − 2x).

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(b) Find all positive values of x such that V(x)> 0, and sketch the graph of V for x > 0.