Problem 1 Let a,b∈R,f(x)=ax+b+9x.a,b \in \mathbb R,f(x)=ax+b+\frac{9}{x}.a,b∈R,f(x)=ax+b+x9. Prove that there exists x0∈[1,9],x_0 \in \left[1,9 \right],x0∈[1,9], such that ∣f(x0)∣≥2.|f(x_0)| \ge 2.∣f(x0)∣≥2.