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Let f:[0,1]rarrR be a function. Suppose ...

Let `f:[0,1]rarrR` be a function. Suppose the function `f` is twice differentiable, `f(0)=f(1)=0` and satisfies `f\'\'(x)-2f\'(x)+f(x) ge 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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