Let f be a twice-differentiable function on R such that f′′ is continuous. Prove that f(x)f′′(x)<0 cannot hold for all x. I have been able to think of specific examples of f(x) in which f(x)f′′(x)<0 does not hold, but I have not been able to come up with specific values of x for which f(x)f′′(x)<0 does not hold. Any help is greatly appreciated!