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The function x^x is increasing when...

The function `x^x` is increasing when

A

`x gt 1/e`

B

`x lt 1/e`

C

`x lt 0`

D

`AA xx in R`

Text Solution

Verified by Experts

The correct Answer is:
A
We have `,y =x^(x) `
`(dy)/(dx) =x^(x) (1+log x)`
For increasing ` (dy)/(dx) gt 0`
` x^(x) (1+log x) lt 0`
` Rightarrow x gt e^(-1)`
` Rightarrow x gt 1/e`
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