The function $f\left( x \right) = {x^{1/x}}$ is

Increasing in $\left( {1,\;\infty } \right)$

Decreasing in $\left( {1,\;\infty } \right)$

Decreasing in $\left( {1,\;e} \right)$ and increasing in $\left( {e,\;\infty } \right)$

JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Hard

1 of 1

Analyzing +4 | -1

The function

f\left( x \right) = {x^{1/x}}

View answer and explanation

Correct option: C

Increasing in

\left( {1,\;e} \right)

and decreasing in

\left( {e,\;\infty } \right)

Option C (Increasing in (1, e) and decreasing in (e,

\infty

)) is correct because the derivative of the function is positive in (1, e) and negative in (e,

\infty