   Chapter 4.8, Problem 3E ### 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

# Suppose the tangent line to the curve y = f(x) at the point (2, 5) has the equation y = 9 − 2x. If Newton’s method is used to locate a root of the equation f(x) = 0 and the initial approximation is x1 = 2, find the second approximation x2.

To determine

To find: The second approximation x2.

Explanation

Given:

The tangent line to the curve y=f(x) at the point (2,5) is y=92x.

Initial approximations are x1=2,f(x1)=5.

Calculation:

Calculate the derivative of y.

dydx=d(92x)dx=2

Calculate x2 by using Newton’s method

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