是一道英文的For any polynomial fuction of degree n,the nth differe

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是一道英文的
For any polynomial fuction of degree n,the nth differences:
are equal(or constant)
have the same sign as the leading coefficient
are equal to a(nx(n-1)...x2x1),where a is the leading coefficient
希望大家能帮我解释下T T
我一点都看不懂
给到例题.
fourth difference=144
degree 4,leading coefficient 6

对一个n阶多项式函数,它的第n阶导数
相等,或为常数
与首项的系数符号相同,
同时这个n阶导数等于a(nx(n-1)...x2x1),这里a是首项系数.
你给那个例题,如第四阶导数=144
则y=ax^4+bx^3+cx^2+dx+e
y'=4ax^3+3bx^2+2cx+d
y''=12ax^2+6bx+2c
y'''=24ax+6b
y''''=24a=144
解得a=6
所以当n=4的时候,首项系数a=6

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