The function x^x decreases in the interv...

The function `x^x` decreases in the interval (a) `(0,e)` (b) `(0,1)` (c) `(0,1/e)` (d) none of these

A

(0,e)

B

(0,1)

C

`(0,(1)/(e ))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:

3

`f(x) = x^(x)[1+logx]=x^(x) log (ex)`
`f(x)lt0`
or `log(ex)lt0`
or `0ltexlt1`
or `0ltexxle1//e`

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