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The figure shows the graph of a function $f .$ Suppose that Newton's method is used to approximate the root $r$ of the equation $f(x)=0$ with initial approximation $x_{1}=1$(a) Draw the tangent lines that are used to find $x_{2}$ and $x_{3}$ and estimate the numerical values of $x_{2}$ and $x_{3}$ .(b) Would $x_{1}=5$ be a better first approximation? Explain.

(a) $x_{2}=2.6 ; x_{3}=3.1$(b) $x_{2}=1.8 .$ since the value of the solution is lesser than what we received in part $(\mathrm{a}), x_{1}=5$ is a bad approximation.

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

Lectures

04:40

In mathematics, a derivati…

30:01

In mathematics, the deriva…

00:50

The figure shows the graph…

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For each initial approxima…

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Finding roots with Newton&…

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(a) Use Newton's meth…

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If $ f(x) = \left\{

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Use Newton's method w…

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Suppose the tangent line t…

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Find the linear approximat…

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Linear approximation and c…

this question asks us to graft and then analyze whether the tension is could be a better approximation. We know that we draw our curve that looks something like this and then we know that are tangent could be like this she can see except ooze two point sex and an ex of three is 3.1 approximately okay for part B, What we know is that given the first approximation exes five, we know that acts of two would give us 1.8 and in part a the first slide to this question we had gotten exit twos. 2.6 one point is smaller than 2.6. Therefore, this is not a good approximation because the solution is smaller than what we received in part egg. The answer is excellent as five is bad approximation.

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