关于曲线f(x)=(x-a_1)^(k_1)(x-a_2)^(k_2)…(x-a_n)^(k_n)拐点的探讨

Study on Inflection Points of f(x)=(x-a_1)^(k_1)(x-a_2)^(k_2)…(x-a_n)^(k_n)

通过分析多项式函数的实重根及其导数的性质,结合罗尔定理和泰勒公式,给出了分析曲线f(x)=(x-a_1)^(k_1)(x-a_2)^(k_2)…(x-a_n)^(k_n)拐点的一般方法 ,指出了在实数域内可以分解的多项式函数全部拐点的分布范围.

By analyzing the real roots of polynomials and its derivative properties,combining the Rolle＇s theorem and the Taylor formula,we give a general method for analysis of the distribution range of inflection points on the curve f（x）=（x-a1）^（k1）（x-a2）^（k2）…（x-an）^（kn）.Furthermore,our method can be successfully used to obtain the distribution of all inflection points for the polynomial function which can be factored in the real domain.