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) when at x = c -...$\ Let\ \alpha$ and $\beta$ respectively be the maximum and the minimum values of the function$$\begin{matrix} f(\theta)...Which of the following function has a maximum at origin ?...If f(x) = , then-...Two parts of 64 such that the sum of their cubes is minimum will be-...