The Inflection Point of a Curve

Based on the definitions of the strict lower convex curve,the strict lower concave curve and the inflection curve,this paper first makes a summary of the necessary condition for a point in a curve being an inflection point,and then proves the ways to determine whether the point whose second derivative is zero when determined by second derivative,third derivative and nth derivative and the point whose second derivative does not exist are both inflection points,and finally makes a conclusion that a point in a curve cannot be both an inflection point and an extreme point.