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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?

A

A) `0ltf(x)ltoo`

B

B) `-(1)/(2)ltf(x)lt(1)/(2)`

C

C) `-(1)/(4)ltf(x)lt1`

D

D) `-ooltf(x)lt0`

Text Solution

Verified by Experts

The correct Answer is:
D
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