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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]`.
If the function `e^(-x)f(x)` assumes its minimum in the interval `[0,1]` at `x=1/4`, which of the following is true?

A

A) `f'(x)ltf(x),(1)/(4)ltxlt(3)/(4)`

B

B) `f'(x)gtf(x),0ltxlt(1)/(4)`

C

C) `f'(x)ltf(x),0ltxlt(1)/(4)`

D

D) `f'(x)ltf(x),(3)/(4)ltxlt1`

Text Solution

Verified by Experts

The correct Answer is:
C
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