Question

Interval in which X^x is strictly increasing is

(1) (0, ∞)

(2) \(\left(0,\frac {1}{e}\right]\)

(3) \(\left[\frac {1}{C^2}, \infty \right)\)

(4) \(\left[\frac {1}{e}, \infty\right]\)

Answer 1

Correct option is (4) \(\left[\frac {1}{e}, \infty\right]\)

Let f(x) = X^x

⇒ f(x) = X^x (1 + lnx)

For strictly increasing, f(x) > 0

⇒ 1 + lnx > 0

⇒ x > 1/e