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f(x)=ax+b+\frac{9}{x}

Source: China second round 2018 (B) Q1

June 22, 2019
algebra

Problem Statement

Let a,b∈R,f(x)=ax+b+9x.a,b \in \mathbb R,f(x)=ax+b+\frac{9}{x}. Prove that there exists x0∈[1,9],x_0 \in \left[1,9 \right], such that ∣f(x0)∣≥2.|f(x_0)| \ge 2.
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