Problem

Formulating Newton's method Write the formula for…

02:31

Problem 5 Easy Difficulty

Formulating Newton's method Write the formula for Newton's method and use the given initial approximation to compute the approximations $x_{1}$ and $x_{2}.$
$$f(x)=x^{2}-6 ; x_{0}=3$$

Answer

$$x_{1}=2.5, x_{2}=2.45$$

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Calculus 1 / AB

Calculus for Scientists and Engineers: Early Transcendental

Chapter 4

Applications of the Derivative

Section 8

Newton's Method

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Video Transcript

we want to use Nunes method to find except one. And except to when F of X is equal to X squared minus six and accept zero is equal to three. Now we can see that F prime of eggs is simply going to be two X. And now let's remind ourselves of the Newmans formula, which states that X of and plus one is equal to x oven minus f of ex event divided by have a fine of ex event now except one is gonna be except zero, which is three minus f of three. Divided by of crime of three f of free. That's gonna be three squared, minus six. So that's gonna be nine months, six or three. As for the denominator f prime of axes, just two acts. So have prime Three is gonna be six, which means this is gonna be free minus 1/2 or 2.5. Now, let's find exit, too, except to it is going to be 2.5 minus breath of 2.5. Divided by have crime of 2.5 now F of 2.5 is going to be 2.5 squared, which is 6.25 minus six. So that's gonna be a 0.25 here in the numerator and for the denominator F prime of 2.5 is going to be 2.5 times to was just just five. So you had 2.5 minus 0.25 divided by five, which is 2.5 minus 0.0 if I, which is that equal to 2.45 So those are answers except one is equal to 2.5 and accept two is equal to 2.45

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