   Chapter 2.7, Problem 36E ### 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 ) = 4 1 − x

To determine

To find: The derivative of the function f(x)=41x 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 square formula: (a2b2)=(a+b)(ab).

Calculation:

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

Compute f(a) by using the equation (1).

f(a)=limh0f(a+h)f(a)h=limh041(a+h)41ah=limh041a41(a+h)1a1(a+h)h=limh04(1a1(a+h))h1a1(a+h)

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

f(a)=limh04(1a1(a+h))h1a1(a+h)×(1a+1(a+h))(1a+1(a+h))

Apply the difference of squares formula,

f(a)=limh04((1a)2(1(a+h))2)h1a1(

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