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Chapter 2.1, Problem 35E
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### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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### Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem
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# Find f ′ ( a ) . f ( x ) = 1 − 2 x

To determine

To find: f'a

Explanation

Given:  fx=1-2x

Formula:

f'a=limh0fa+h-f(a)h

a2-b2=a+b(a-b)

Calculation:

Consider f'a=limh0fa+h-f(a)h

Substitute the values of f (a + h) and f (a) in the formula to get

f'a=limh01-2(a+h)-1-2ah

To rationalize the numerator, multiply numerator and denominator by the conjugate (1-2a+h+1-2a).

Thus we have

f'a=limh0(1-2a+h-1-2a)(1-2a+h+1-2a)h(1-2a+h+1-2a)

Using the identity  a2-b2=a+b(a-b)

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