1.

The function `f(x)=x^(x)` has a stationary point atA. x=eB. x`=1/e`C. x=1D. `x=sqrt( E)`

Answer» Correct Answer - B
We have, `f(x)= x^(x)`
Let `y=x^(x)`
and log `y=x logx`
`therefore 1/y.(dy)/(dx)=x.1.x+log x.1`
`rArr (dy)/(dx)=(1+logx).x^(x)`
`therefore (dy)/(dx)=0`
`therefore (dy)/(dx)=0`
`rArr (1+logx).x^(2)=0`
`rArr log x=-1`
`rArr logx=loge^(-1)`
`rArr x=e^(-1)`
`rArr x=1/e`
Hence, f(x) has a stationary point at `x=1/e`


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