Chapter 2.7, Problem 11E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

(a) A company makes computer chips from square wafers of silicon. It wants to keep the side length of 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′(15) 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

To determine

**Part (a):**

**To find:**The rate of change of the area A(x) that means how the area A(x) of a wafer changes when the side length x changes then find A’ (15) and explain its meaning in given situation.

Explanation

**1) Concept**

Use concept of derivative to find the rate of change of the area A.Here

**2) Formula:**

i) The area of a square with side length x is,

ii) Power Rule:

**3) Given:**

A company makes computer chips from square wafers of silicon and the side length of a wafer very close to 15 mm that means x = 15 mm.

**4) Calculation:**

To find

Thus, the rate of change of area Aâ€™(x) = 2x

To find

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