The Newton-Raphson algorithm is applied to estimate a zero of f(x) with $x 0$ = 3. Which of the following statements is true?
A) $\mathrm { x } _ { 1 }$ = 3 - $\frac { f ^ { \prime } ( 3 ) } { f ( 3 ) }$
B) $\mathrm { x } _ { 1 }$ = 3 + $\frac { f ^ { \prime } ( 3 ) } { f ( 3 ) }$
C) $\mathrm { x } _ { 1 }$ = 3 - $\frac { f ( 3 ) } { f ^ { \prime } ( 3 ) }$
D) $\mathrm { x } _ { 1 }$ = $\frac { f ^ { \prime } ( 3 ) } { f ( 3 ) }$
E) none of these

Question

Quizplus · Accepted Answer

The Newton-Raphson formula for finding successively better approximations to the roots (or zeroes) of a real-valued function is $x_{n+1} = x_n - \frac{f(x_n)}{f'(x_n)}$. Therefore, the correct formula for the first iteration starting from $x_0 = 3$ is $x_1 = 3 - \frac{f(3)}{f'(3)}$, which matches option C.

The Newton-Raphson Algorithm Is Applied to Estimate a Zero of F(x)