Maxima and MinimaHard

Question

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

Options

A.e
B.(e)1/e
C.(1/e)e
D.ee

Solution

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

fMax = (1/1/e)1/e = e1/e

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