Use Newton's Method to approximate the x-value of the indicated point intersection of the two graphs accurate to three decimal places.
A) 0.371
B) 0.363
C) 0.356
D) 0.359
E) 0.352

Question

​Use Newton's Method to approximate the x-value of the indicated point intersection of the two graphs accurate to three decimal places. ​   ​ 
A) ​0.371 
B) ​0.363 
C) ​0.356 
D) ​0.359 
E) ​0.352

Quizplus · Accepted Answer

Using Newton's Method, we start with an initial guess of $x_1 = 0.4$ (approximate point of intersection). Then we have:
\begin{align*}
f(x) &= x^3-2x^2-5x+6\
f'(x) &= 3x^2-4x-5\
x_2 &= x_1 - \frac{f(x_1)}{f'(x_1)}\
&= 0.4 - \frac{0.064}{1.1}\
&= 0.345\
x_3 &= x_2 - \frac{f(x_2)}{f'(x_2)}\
&= 0.345 - \frac{0.00453}{0.612}\
&\approx 0.363
\end{align*}
Therefore, choice B is the best option, being accurate to three decimal places.

​Use Newton's Method to Approximate the X-Value of the Indicated

Use Newton's Method to Approximate the X-Value of the Indicated