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Let f[0, 1] -> R (the set of all real n...

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 le f(x) le oo`

B

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

C

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

D

`-oo le f(x) le 0`

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The correct Answer is:
D
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