Question

The function f(x) = x^x has a stationary point at

(a) x = e

(b) x = \(\frac 1e\)

(c) x = 1

(d) x = \(\sqrt e\)

Answer 1

Correct option is (b) x = \(\frac 1e\)

f'(x) = x^x(1 + logx)

For Stationary point

f'(x) = 0

x^x(1 + logx) = 0

⇒ logx = -1

⇒ x = e^-1 = \(\frac 1e\)