Question

The maximum value of (1/x)^x is:

A. e
B. e^e
C. c^1/e
D. (1/e)^1/e

Answer 1

Now applying the product rule of differentiation we get

Now we will find the critical point by equating equation (i) to 0, we get

Hence f(x) has a stationary point at x = 1/e.

i.e the maximum value of f(1/e) = e^1/e

So the correct option is option C.