A Derivative Sum at Equal Heights

★ 7/10calculus Monotonicity inequality Symmetry

Problem

Let $f(x) = x - 1 - \ln x$ . If distinct positive reals $x_1, x_2$ satisfy $f(x_1) = f(x_2)$ , prove that

f'(x_1) + f'(x_2) < 0.

Answer

Solution

Difficulty	7/10
Topics	calculus, Monotonicity, inequality, Symmetry

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