Question

Let f:[0,1]$\rightarrow$R be a function. suppose the function f is twice differentiable,f(0)=0=f(1) and satisfies f''(x)-2f'(x)+f(x)$\geq$ex,x$\in$[0,1], which of the following is true?

• A. 0<f(x)<$\infty$
• B. $-\frac{1}{2}<f(x)<\frac{1}{2}$
• C. $-\frac{1}{4}<f(x)<1$
• D. $-\infty<f(x)<0$

Answer 1

Answer: (D)

$-\infty<f(x)<0$

Answer 2

The correct answer is option (D) : $-\infty<f(x)<0$