1-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.

V(x) =

(b) Find the values of x for which the volume is greater than 200 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.)
=? in3

2-A rancher wants to build a rectangular pen with an area of 36 m2.

(a) Find a function that models the length F of fencing required, in terms of the width w of the pen.
F(w) =

(b) Find the pen dimensions that require the minimum amount of fencing.

width =? m
length=? m