Show that the maximum value of `(1/x)^x` is `e^(1/e)dot`

A

e

B

`e^e`

C

`e^(1/x)`

D

`(1/e)^(1/e)`

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

The value of int(x-1)e^(-x) dx is equal to

The value of int_(0)^(1)x^(2)e^(x)dx is equal to

If the function f(x) =log x, x in (1, e) , satisfies all the conditions of LMVT, then the value of c is..... A) 1 B) e C) 1/e D) e-1

The second order derivative of (e^x+1)/e^x is

For the function f(x) = (log_(e )(1+x)-log_(e )(1-x))/(x) to be continuous at x = 0, the value of f(0) should be

Solution of the differential equation (1+e^(x/y))dx + e^(x/y)(1-x/y)dy=0 is

The value of int_(1)^(e^(2)) (dx)/(x(1+logx)^(2)) is