A graphing calculator is recommended. In this problem you are asked to find a fu

Question

A graphing calculator is recommended.

In this problem you are asked to find a function that models a real-life situation and then use the model to answer questions about the situation. Use the guidelines on page 237 to help you.

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides (see the figure).

(a) Find a function that models the volume V of the box.

(b) Find the values of x for which the volume is greater than 230 in3. (Round your answers to three decimal places. Enter your answer using interval notation.)

(c) Find the largest volume that such a box can have. (Round your answer to three decimal places.)

Explanation / Answer

a. Let x square inches cut off at each corners

V=x(14-2x)(30-2x)

b.230=x(14-2x)(30-2x)

x=0.628in

c. V=x(14-2x)(30-2x)

V'=4x3-88x2+420x

V'=0

12x2-176x+420=0

x=3

V=3(14-6)(30-6)=576square inches

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