The Linear Approximation $L ( x )$ To $f ( x ) = e ^ { - x }$

Multiple Choice

The linear approximation $L ( x )$ to $f ( x ) = e ^ { - x }$ near $x _ { 0 } = 1$ is

A) $\frac { 1 } { e ^ { ( x - 1 ) } }$
B) $\frac { 1 } { e } ( x - 2 )$
C) $\frac { 1 } { e } - ( x - 1 )$
D) $\frac { 1 } { e } ( 2 - x )$
E) $\frac { 1 } { e } + ( x - 1 )$