Question

Let f be the differentiable for ∀ x. If f(1) = – 2 and f '( x ) ≥ 2 for [1, 6], then
(a) f(6) < 8 

(b) f(6) ≥ 8

(c) f(6) = 5 

(d) f(6) < 5.

Answer 1

(b) : Let if possible f '(x) = 2 for
=> f(x) = 2x + c (Integrating both side w.r.t. x)
∴f(1) = 2 + c, –2 = 2 + c
=> c = – 4 ∴ f(x) = 2x – 4
∴ f(6) = 2 × 6 – 4 = 8 ∴ f(6) ≥ 8.