Suppose Sarah is trying to design a metal box (a rectangular prism), which will

Question

Suppose Sarah is trying to design a metal box (a rectangular prism), which will hold 430 cubic centimeters of liquid. The length of the box must be 3 times as large as the width. a. 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 Preview Se box as the width of the box increases from 2 to 14 centimeters. Preview c. 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 7.7 to 14.2 centimeters. Preview

Explanation / Answer

volume of the box = 430 cubic centimeters

length = 3 * width

length * width * height = 430

3 w * w * h = 430

j = 430 / 3w^2

b) width increases from 2 to 14 cm

j (2) = 430 / 3 (2)^2 = 430 / 12

j(14) = 430 / 3(14)^2 = 430 / 588

change in the height = 430/12 - 430 / 588

c) average rate of change = j(14.2) - j(7.7) / ( 14.2 - 7.7)

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