1) Let f'(x) , be differentiable ∀x . if f(1)=-2 and f′(x)≥2∀x∈[1,6], then A) f(6) < 8 B) f(6) ≥ 8 C) f(6) ≥ 5 D) f(6) ≤ 5 Answer: Option BExplanation: f'(x) is differentiable ∀x∈[1,6] By Lagrange's mean value theorm f′(x)=f(6)−f(1)6−1 f′(x)≥2∀x∈[1,6] (given) ⇒ f(6)+25≥2 [∵ f(1)=-2] \Rightarrow f(6) \geq 10-2 \Rightarrow f(6) \geq 8