Question

Let f : [1/2 ,1] → R (the set of all real numbers) be a positive, non-constant and differentiable function such that f'(x) < 2f(x) and f(1/2) = 1. Then the value of \(\int\limits_{1/2}^1\) f(x) dx lies in the interval

(A) (2e - 1, 2e)

(B) (e - 1, 2e - 1)

(C) (e-1/2 , e - 1)

(D) (0, e - 1/2)

Answer 1

(D) (0, e - 1/2)

Given f'(x) – 2f (x) < 0