F:R-->R, the fourth derivative of f is continuous for all x... 1. The problem statement, all variables and given/known data Suppose f is a mapping from R to R and that the fourth derivative of f is continuous for every real number. If x is a local maximum of f and f"(x)=0 (the second derivative is zero at x), what must be true of the third derivative at x? Fully justify your answer. 3. The attempt at a solution my thinking so far is that since the forth derivative is continuous for every real number, it should exists for every real number. If the forth derivative exists, it means that the third derivative is continuous for every real number (since we know that if derivative of f exists at a point x, then f is continuous at that point). so all I know is that the third derivative is continuous at every point including point x.