51问答网 > 设函数f(x)=(x-1)(x-2)(x-3)(x-4),则f✀(x)=0有

设函数f(x)=(x-1)(x-2)(x-3)(x-4),则f✀(x)=0有

2024-12-23 02:25:58

推荐回答（2个）

回答1：

1、因为f(x)=(x-1)(x-2)(x-3)(x-4)的根是x=1,2,3,4
画图易知f'(x)=0的三个根,分别位于区间(1,2),(2,3),(3,4)内
2、
lny=ln(x-1)(x-2)(x-3)(x-4)=ln(x-1)+ln(x-2)+ln(x-3)+ln(x-4)
(lny)'=(1/y) *y'=1/(x-1 )+1/(x-2)+1/(x-3)+1/(x-4)
f'(x)=y'={1/(x-1 )+1/(x-2)+1/(x-3)+1/(x-4)}*{(x-1)(x-2)(x-3)(x-4)}
=(x-2)(x-3)(x-4)+(x-1)(x-3)(x-4)+(x-1)(x-2)(x-4)+(x-1)(x-2)(x-3)
该函数是三次有三个根排除B、C
然后判断f'(0)f1(1)的符号都小于0 所以选A

回答2：