   Chapter 3.7, Problem 11E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# (a) A company makes computer chips from square wafers of silicon. It wants to keep the side length o f a wafer very close to 15 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes. Find A′(l5) and explain its meaning in this situation.(b) Show that the rate of change of the area of a square with respect to its side length is half its perimeter. Try to explain geometrically why this is true by drawing a square whose side length x is increased by an amount ∆x. How can you approximate the resulting change in area ∆A if ∆x his small?

(a)

To determine

To find: The value of A(15).

Explanation

Given:

The company makes square wafers of silicon of area of the form A(x)=x2.

Calculation:

Differentiate the area of the square wafer respect to x.

A(x)=x2

A'(x)=2x

Substitute 15 for x in the above equation and find A

(b)

To determine

To Show: The rate of change of the area of a square with respect to the change in its side length is equal to half its perimeter.

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 