Question

The function f(x) = x^x is decreasing in

• A. (0, e)
• B. (0,1)
• C. (0, 1/e)
• D. None of these

Answer 1

Answer: (C)

(0, 1/e)

Answer 2

f(x) = x^x Æ

$\Rightarrow \mathrm { f } ^ { \prime } ( \mathrm { x } ) = \mathrm { x } ^ { \mathrm { x } } ( \log \mathrm { x } + 1 ) < 0$

Ž log x + 1 < 0 Ž x < $\frac{1}{e}$also 0 < x < $\frac{1}{e}$