The Linear Approximation $L ( x )$ To $f ( x ) = \sqrt { x }$

Multiple Choice

The linear approximation $L ( x )$ to $f ( x ) = \sqrt { x }$ near $x _ { 0 } = \frac { 1 } { 4 }$ is

A) $- \frac { 1 } { 2 } + \left( x + \frac { 1 } { 4 } \right)$
B) $- \frac { 1 } { 2 } - \left( x - \frac { 1 } { 4 } \right)$
C) $\frac { 1 } { 2 } - \left( x - \frac { 1 } { 4 } \right)$
D) $- \frac { 1 } { 2 } + \left( x - \frac { 1 } { 4 } \right)$
E) $\frac { 1 } { 2 } + \left( x - \frac { 1 } { 4 } \right)$