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