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Let `f[0, 1] -> R` (the set of all real numbers be a function.Suppose the function f is twice differentiable, `f(0) = f(1) = 0`,and satisfies `f'(x) – 2f'(x) + f(x) leq e^x, x in [0, 1]`.Which of the following is true for `0 lt x lt 1 ?`

A

`0 lt f(x) lt infty`

B

`-1/2 lt f(x) lt 1/2`

C

`-1/4 lt f(x) lt 1`

D

` -infty lt f(x) lt 0`

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The correct Answer is:
D
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