1. The problem statement, all variables and given/known data Let f:[0,1]→R be a function. Suppose the function f is twice differentiable, f(0)=f(1)=0 and satisfies [itex]f"(x)-2f'(x)+f(x)≥e^x[/itex], x:[0,1]. Then find range of f(x). 3. The attempt at a solution Strictly speaking, this has been one of the toughest problems I've ever encountered throughout my course in Calculus. So, obviously I don't have an idea where to start with. But atleast, from the given information, I can say that f'(x) must be zero somewhere in [0,1] according to Rolle's Theorem. Since the inequation also involves a second order derivative, finding a solution of this differential inequation (never heard of diff. inequation btw) is beyond my reach.