   Chapter 2.7, Problem 35E ### 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

# Find f'(a). f ( x ) = 1 − 2 x

To determine

To find: The derivative of the function f(x)=12x at x=a.

Explanation

Formula used:

The derivative of a function f at a number a, denoted by f(a) is,

f(a)=limh0f(a+h)f(a)h (1)

Difference of squares formula: (a2b2)=(a+b)(ab).

Calculation:

Obtain the derivative of the function f(x) at x=a.

Use the equation (1) to compute f(a),

f(a)=limh0f(a+h)f(a)h=limh0(12(a+h))(12a)h

Multiply both the numerator and the denominator by the conjugate of the numerator,

f(a)=limh0(12(a+h))(12a)h×(12(a+h))+(12a)(12(a+h))+(12a)=limh0((12(a+h))(12a))×((12(a+h))+(12a))h((12(a+h))+(12a))<

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