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Let f : ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ 1 , 2 1 → R (the set of all real numbers) be a positive, non-constant and differentiable function such that f '(x) < 2 f(x) and ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ 2 1 f = 1. Then the value of ∫ 1 2 / 1 dx ) x ( f lies in the interval -

1. (2e – 1, 2e)
2. (e – 1, 2e – 1)
3. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − − 1 e , 2 1 e
4. ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 2 1 e , 0

Correct answer: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − 2 1 e , 0

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