   Chapter 4.8, Problem 13E ### 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.3x4 − 8x3 + 2 = 0, [2, 3]

(a)

To determine

To explain: About the presence of root of the given equation in the interval [2,3].

Explanation

Given:

The function is f(x)=3x48x3+2.

The closed interval [2,3].

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 f(x).

f(2)=3×(2)48(2)3+2=3×168×

(b)

To determine

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

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In problems 24-26, find the intercepts and graph. 24.

Mathematical Applications for the Management, Life, and Social Sciences

#### Verify directly that n(AB)=n(A)+n(B)n(AB) for the sets in Exercise 3.

Finite Mathematics for the Managerial, Life, and Social Sciences

#### For f(x) = x3 + 7x, df = _____. a) (x3 + 7x) dx b) (3x2 + 7) dx c) 3x2 + 7 d) x3 + 7x + dx

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