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Show that the maximumvalue of `(1/x)^x`is `e^(1//e)`.A. eB. `e^( e)`C. `e^(1//e)`D. `(1/e)^(1//e)` |
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Answer» Correct Answer - C Let `y=(1/x)^(x)` `rArr logy=x.log1/x` `therefore 1/y(dy)/(dx)=x.1/(1/x). (-1/x^(2))+ log 1/x.1` `=-1+log1/x` `therefore (dy)/(dx)= (log 1/x-1).(1/x)^(x)` Now, `(dy)/(dx)=0` `rArr log1/x=1=loge` `rArr 1/x=e` `x=1/e` Hence, the maximum value of `f(1/e)=(e)^(1//e)` |
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