Suppose Sarah is trying to design a metal box a rectangular

Suppose Sarah is trying to design a metal box (a rectangular prism), which will hold 350 cubic centimeters of liquid. The length of the box must be 3 times as large as the width.

1. Define a function j that gives the height of the metal box, h, measured in centimeters in terms of the width of the metal box, w, measured in centimeters.

2. Use function notation to represent the change in the height of the box as the width of the box increases from 4 to 15 centimeters.

3. Use function notation to represent the average rate of change of the height of the box with respect to the width of the box as the width of the box increases from 7.6 to 15.1 centimeters.

Solution

1) length of the box must be 3 times as large as the width.

lenght = 3*w

Volume = l*w*h = 3w*w*h

350 = 3w^2*h

h = 350/3w^2

2) change in height = 350/3[ 1/15^2 - 1/4^2]

3) Rate of change of heiht w.r.t width

dh/dw = -700/3w^3

dh = dw(-700/3w^3)

= (15.1 - 7.6)( -700/3*7.6^3 )