Question

When x is positive, the minimum value of x^x is

A. e^e

B. e^1/e

C. e^-1/e

D.(1/e)

Answer 1

Answer is : C. e^-1/e

Given: f(x) = x^x.

⇒ f' (x) = (log x+1) x^x

⇒ keeping f’(x) = 0

We get

When x is greater than zero,

 We get a maximum value as the function will be negative.

Therefore,

F(x) = x^x

F(e) = (1/e)^1/e = e^-1/e

Hence, C is the correct answer.