高次多项式函数的“平行性”问题

The"Parallelism"of Higher Order Polynomial

通过研究二次函数的割线斜率与切线斜率相等即割线与切线相互平行,得到的条件为:该二次函数与割线两交点的横坐标数值的平均值等于该二次函数与切线切点的横坐标数值.进而将二次函数的这种切割线“平行”特性推广到高次多项式函数.采用数值均差法证明了由二次函数的切割线“平行”特性推广到高次多项式函数后的结论,此结论与高次多项式的最高次数和导数阶数有关.

By studying that the secant slope and the tangent slope of the quadratic function are equal,that is,the secant and the tangent are parallel to each other,the obtained condition is that the average value of the transverse coordinate value of the intersection point of the quadratic function and the secant is equal to the transverse coordinate value of the tangent point of the quadratic function.Furthermore,this"Parallel"property of the quadratic function is extended to the higher order polynomial.By means of the numerical mean difference method,the conclusion that the"Parallel"property of the cutting line of the quadratic function is extended to the higher order polynomial is proved,which is related to the highest order of the higher order polynomial.