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

Create a free account to view solution

View Solution Free

Topic: Maxima and Minima·Practice all Maxima and Minima questions

More Maxima and Minima Questions

f(c) is a maximum value of f(x) if -...Read of the following mathematical statements carefully :I. A differentiable function ′f′ with maximum at x ...If value of the function a2 sec2 θ + b2 cosec2 θ (a > 0, b > 0) is minimum, then θ equals -...The rate of change of the function f(x) = 3x5 - 5x3 + 5x - 7 is minimum when...The point of maxima of sec x is -...