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

A

e

B

`e^(e)`

C

`e^(1//e)`

D

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

Verified by Experts

The correct Answer is:

C

Similar Questions

Explore conceptually related problems

Show that the value of x^(x) is minimum when x=(1)/(e)

Prove that (1/x)^(x) has maximum value is (e)^(1/e) .

The maximum value of x^((1)/(z)),x>0 is (a) e^((1)/(e))(b)((1)/(e))^(e)(c)1(d) none of these

Show that (log x)/(x) has a maximum value at x=e

Find the maximum value of the function x * e^(-x) .

The maximum value of (log x)/(x) is (a) 1 (b) (2)/(e)(c) e (d) (1)/(e)

The maximum value of x^(4)e^(-x^(2)) is (A) e^(2)(B)e^(-2)(C)12e^(-2)(D)4e^(-2)

The minimum value of (x)/((log)_(e)x) is e(b)1/e(c)1(d) none of these

Show that the function f(x) given by f(x)={(e^(1/x)-1)/(e^(1/x)+1), when x!=00,quad when x=0 is discontinuous at x=0

The minimum value of x(log)_(e)x is equal to e (b) 1/e(c)-1/e (d) 2e( e )e