VITEEE 2014 Paper

f'(x) is differentiable for all x ∊ [1,6]
By Lagrange’s mean value theorem,
f ' (x) =

f(6)−f(1)

6−1

f ' (x) ≥ 2 for all x ∊ [1 , 6] (given)
⇒

f(6)+2

5

≥ 2 [Since f (1) = - 2]
⇒ f (6) ≥ 10 - 2 ⇒ f (6) ≥ 8