Discrimination on False Inflection Point of Curves

When the second derivative y″(x) of function of a curve given by parameter equation has different signs on two sides of a certain parameter value t0,the corresponding point determined may be a false inflection point.The reason why the false inflection point is erroneously claimed as an inflection point is that the different signs of y″(x) on the two sides of t0 is regarded as the different signs of y″(x) on the two sides of x0.The solution is that the characteristic of the tangent line at any inflection point can be utilized to discriminate the true or false inflection point after getting possible inflection points.By using the curvature formula in differential geometry,the curved degree,the curved direction and the inflection point of a curve can be identified together.