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

The Correct Option is D

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