1. The problem statement, all variables and given/known data Let f(x) be a twice differentiable function on an interval I. Let f''(x)>0 for all x in I and let f'(c)=0 for some c in I. Prove f(x) is greater than or equal to f(c) for all x in I. 2. Relevant equations Mean value theorem? 3. The attempt at a solution f''(x)>0 implies that f'(x) is strictly increasing on I. I don't know what to use the f'(c)=0 for, and whether or not to use the mean value theorem.