   Chapter 3.8, Problem 13E

Chapter
Section
Textbook Problem

# 13-14 (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. 3 x 4 − 8 x 3 + 2 = 0 ,    [ 2 , 3 ]

To determine

a)

To explain:

How we know that the given equation must have a root in the interval

Explanation

1) Concept:

Intermediate value theorem- If a continuous function f with an interval [a,b] as its domain takes values fa and fb at each end point of the interval then it also takes any value between fa and fb  at some point within the interval.

2) Given:

The equation 3x4-8x3+2=0 and [2,3]

3) Calculation:

Let fx=3x4-8x3+2

Since fx is a polynomial function then it is continuous

So fx continuous on [2,3]

So by Substituting a=2 and b=3 in f

To determine

b)

To use:

TheNewton’s method to approximation the root correct to six decimal places

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