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 dimensions14in. by30in. by cutting out equal squares of sidexat each corner and then folding up the sides (see the figure).3014

(a) Find a function that models the volumeVof the box.

V(x) =4x388x2+420x

(b) Find the values ofxfor which the volume is greater than230in³. (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