y=f(x)=ax^3+bx^2+cx+d与x轴有3个交点,则有2个极值点
f'(x)=3ax^2+2bx+c=0有2个根
f(x)在[-1,0]和[4,5]有相同单调性,在[0,2]和[4,5]上有相反单调性
则f(x)在[-1,0]和[0,2]有相反单调性,x=0是一个极值点
f(2)=0,另一极值点在(2,4]上
f'(0)=c=0
f'(x)=x(3ax+2b)=0,另一个极值点x=-(2b/3a)
2<(-2b)/(3a)<=4,-6<=b/a<-3
设f'(x)=3ax^2+2bx=3b
3ax^2+2bx-3b=0
△=4b^2+36ab=4b(b+9a)
-6<=b/a<-3,-1/3<a/b<=-1/6,-3<9a/b<=-3/2
-2<9a/b+1<=-1/2,-2<(b+9a)/b<=-1/2
b(b+9a)<0
∴△<0,f'(x)=3b无实数解,
f(x)的图象上不存在一点M,使得f(x)在M的切线斜率为3b
