Find the Minimum Value Of $f ( x ) = x ^ { - \frac { 1 } { x } }$

Multiple Choice

Find the minimum value of $f ( x ) = x ^ { - \frac { 1 } { x } }$ .

A) 0
B) $e ^ { - \frac { 1 } { \ell } }$
C) $e ^ { \frac { 1 } { e } }$
D) e
E) $e ^ { e }$
F) $e ^ { -e }$
G) 1
H) Does not exist