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`

Options

A. g is increasing on `(1,oo)`
B. g is decreasing on `(0,1)`
C. g is increasing on (1,2) and decreasing on `(2,oo)`
D. g is decreasing on (1,2) and increasing on `(2,oo)`

Answer

B