The maximum value of `f(x)=(logx)/(x)(x ne 0, x ne1)` is

Options

A. e
B. `1/e`
C. `5`
D. `10`

Answer

B

Explanation

Given, `f(x) =(logx)/(x) "…"(i)`
On differentiating both sides w.r.t.x, we get
`f'(x) = (x.(1)/x - log x.1)/(x^(2)) = (1-logx)/(x^(2))`
For maximum or minimum value, put `f'(x) = 0`
`(1-logx)/(x^(2)) = 0`
`rArr log x = 1 rArr x = e`
On substituting `x =e` in Eq. (i) , we get
`f(x) = (loge)/(e) = 1/e lt 0`
`:.` Maximum value of `f(x)` i `1/e` at `x = e`.