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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

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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.

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### Video Transcript

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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