find the maximum and minimum value of f(x) = log x/x

Dear Student,
Please find below the solution to the asked query:

We have:y=logxxdydx=x.ddxlogx-logx.ddxxx2=x.1x-logxx2dydx=1-logxx2For maxima or minima dydx=01-logxx2=01-logx=0logx=1x=e1=eNowlogx>1 when x>eandlogx<1 when x<edydx>0 increases when x<e and dydx<0 decreases when x>e, hence x=e will be point of local maxima.And as fx has only one critical point hence minimum value will tend towards -.fx=logxxfxmax=logeefxmax=1e 

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