f(x) = xx has a stationary point at ______.

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f(x) = xx has a stationary point at x = 1/"e". Explanation: We have f(x) = xx Taking log of both sides, we have log f(x) = x log x Differentiating both sides w.r.t. x, we get `1/("f"(x)) * "f'"(x) = x * 1/x + log x * 1` $\Rightarrow$ f'(x) = f(x)[1 + log x] = xx[1 + log x] To find stationary point, f'(x) = 0 $\therefore$ xx[1 + log x] = 0 xx $\neq$ 0 $\therefore$ 1 + log x = 0 $\Rightarrow$ log x = – 1 $\Rightarrow$ x = e–1 $\Rightarrow$ x = 1/"e"

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