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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

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.

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