The differentiable function f(x) is said to have a stationary point at x = a when f^(1) (a) = 0. The nature of a stationary point depends upon when the function has the next non-zero derivative. From the Calculus notes, Corollary 4.2.6, we find the following criterion. Classification of Stationary Points Suppose that f^(1) (a) = 0 and n greaterthanorequalto 1 is the smallest positive integer for which f^(n) (a) notequalto 0. Then if n is odd, then f has a horizontal point of inflexion at x = a, if n is even and f^(n) (a) > 0 then f has a local minimum at x = a, if n is even and f^(n) (a)
