   Chapter 4.8, Problem 14E ### 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

# (a) Explain how we know that the given equation must have a root in the given interval. (b) Use Newton’s method to approximate the root correct to six decimal places.−2x5 + 9x4 − 7x3 − 11x = 0, [3, 4]

(a)

To determine

To explain: The given equation have root in the given interval [3,4].

Explanation

Given:

The function is f(x)=2x5+9x47x311x.

The closed interval is [3,4].

Result used:

Intermediate value theorem:

If f is a continuous function in [a,b] and f(a)>0,f(b)<0 or f(a)>0,f(b)<0, then c(a,b) such that f(c)=0.

Calculation:

Substitute the boundary values of the given interval in the function.

f(3)=2(3)5+9(3)47(3)311(3)=2×243+9×817×2711×3=x

(b)

To determine

To approximate: The root of the given equation correct to six decimal places by using Newton’s method.

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Study Guide for Stewart's Multivariable Calculus, 8th 