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Let f:[0,1]rarrR (the set of all real nu...

Let `f:[0,1]rarrR` (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) ge e^x, x in [0,1]` Which of the following is true for `0 lt x lt 1` ? (A) `0 lt f(x) lt oo` (B) `-1/2 lt f(x) lt 1/2` (C) `-1/4 lt f(x) lt 1` (D) `-oo lt f(x) lt 0`

A

`0 f (x) lt oo`

B

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

C

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

D

`-oo lt f(x) lt 0`

Text Solution

Verified by Experts

The correct Answer is:
D
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