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Last active June 8, 2022 14:21
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The last problem of NCEE Math Guangdong 2022 (English translation)
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problem.md

Let $f(x) = e^x - ax$, $g(x) = ax - \mathrm{ln}x$, $f$ shares the minimum with $g$.

  1. Determine $a$
  2. Prove that there exists a line $y = b$, such that there are three different intersections of $y = b$, $y = f(x)$ and $y = g(x)$, and the x-coordinates of these points form an arithmatic sequence
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