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The figure shows the graph of a function $ f $. Suppose that Newton's method is used to approximately the root $ s $ of the equation $ f(x) = 0 $ with initial approximaton $ x_1 = 6 $.(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 = 8 $ be a better first approximation? Explain.

(a) $$x_{2} \approx 7.3 \quad x_{3} \approx 6.8$$(b) 6

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 8

Newton's Method

Derivatives

Differentiation

Volume

Matt S.

July 24, 2021

This doesn't explain much... Wish the video included a description of what is actually going on in the problem, rather than just giving the solution.

Jas S.

October 12, 2021

nothing was explained...

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Okay, a As you can see, they would have tangent ones that look like us. We estimate x two to be 7.15 and expose three to be 6.85 X three is relatively close to us. Okay, Part B. The answer to this would be yes. X one equals a is a better approximation. And using X one equals sex. The value of X three is close to survive s than X three resulting from X one equals sex.

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