Question

f(x) = x^x is decreasing in the interval

A. (0, e)

B. (0, 1/e)

C. (0,1)

D. none of these

Answer 1

Answer is : B. (0, 1/e)

Given: f(x) = x^x .

⇒ f'(x) = (log x+1) x^x

⇒ keeping f’(x) = 0

We get

⇒ x = 0 or x = 1/e

Now When x > 1/e the function is increasing

x < 0 function is increasing.

But in the interval (0,1/e) the function is decreasing.