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

Question

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

Quizplus · Accepted Answer

The minimum value of $f(x)$ is $e ^ { - \frac { 1 } { \ell } }$ because $f(x)$ is a decreasing function for $x > 0$.

Find the Minimum Value Of f(x)=x−1xf ( x ) = x ^ { - \frac { 1 } { x } }f(x)=x−x1​

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