f(x) = xx is decreasing in the intervalA. (0, e)B. (0, 1/e)C. (0,1)D.

1.	f(x) = xx is decreasing in the intervalA. (0, e)B. (0, 1/e)C. (0,1)D. none of these
Answer» 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.

f(x) = xx is decreasing in the intervalA. (0, e)B. (0, 1/e)C. (0,1)D. none of these

Answer»

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.