Question

If f : R → R is a twice differentiable function such that f' (x) > 0  for all x ∈ R, and f(1/2) = 1/2 , f (1) = 1, then 

(A) f '(1) ≤ 0

(B) 0 < f'(1) ≤ 1/2

(C) 1/2 < f'(1) ≤ 1

(D) f' (1) > 1

Answer 1

Correct option is (D) f' (1) > 1

Let h(x) = f(x) – x