1. The problem statement, all variables and given/known data For a generic function y=f(x) which is twice-differentiaable, is it possible for there to be a curvature on the curve of that function that is greater than the curvature at its relative extremum? 2. Relevant equations 3. The attempt at a solution From visualization and a sketch, I would say yes. but I'd like to be able to explain this mathematically. At the maximum, K = (d2y/dx2) since dy/dx=0 at the extremum making the denominator equal to 0.