Suppose $x 0$ Is an Initial Approximation of a Zero of the Function

Multiple Choice

Suppose $x 0$ is an initial approximation of a zero of the function f(x) . Using the Newton-Raphson algorithm, a second approximation, $\mathrm { x } _ { 1 }$ is obtained. Which of the following must be true?

A) $\mathrm { x } _ { 1 }$ is the x-coordinate of the x-intercept of the tangent line to f(x) at $\left( { } { \mathrm { x } } _0 , \mathrm { f } \left( \mathrm { x } _ { 0 } \right) \right)$
B) f( $\mathrm { x } _ { 1 }$ ) = 0
C) $\mathrm { x } _ { 1 }$ = $x _0$ - $\frac { f ^ { \prime } \left( x _ { 0 } \right) } { f \left( x _ { 0 } \right) }$
D) $\mathrm { x } _ { 1 }$ is closer to the zero of f(x) than $x _0$ .
E) all of these