Maxima and MinimaHard

Question

The maximum value of (1/x)^x is-

Options

A.e

B.(e)^1/e

C.(1/e)^e

D.e^e

Solution

f(x) = (1/x)x
lny = xln(1/x) = - xlnx
= - [1 + lnx]
(lnx + 1)

f_Max = (1/1/e)^1/e= e^1/e

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