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JEE Previous Year Question

$f (x) = x^{x} has stationary point at$

Topic: JEE PYQ

Answer: B. Full step-by-step solution below.

A $x = e$
B $x = \frac{1}{e}$
C $x = 1$
D $x = e$

Correct answer: B

Solution

(b) : We have, f (x) = x^{x} \Rightarrow f^{’} (x) = x^{x} (1 + log x) For stationary point, f^{’} (x) = 0 \Rightarrow x^{x} (1 + log x) = 0 \Rightarrow 1 + log x = 0 \Rightarrow log x = - 1 \Rightarrow x = e^{- 1} ∴ x = \frac{1}{e}

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