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Let f : [1/2, 1] rarr R (the set of the ...

Let `f : [1/2, 1] rarr R` (the set of the all real numbers) be a positive, non-constant and differentiable function such that `f'(x) lt 2 f(x)` and `f(1/2) = 1`.Then the volue of `int_(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))`

Text Solution

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The correct Answer is:
D
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