设切点为(t,t^3-2t^2-4t).
切线斜率=(t^3-2t^2-4t-c)/(t-2)
切线斜率=f'(t)=3t^2-4t-4
(t^3-2t^2-4t-c)/(t-2)=3t^2-4t-4
2t^3-8t^2+8t+c+8=0有两个根.
设h(t)=2t^3-8t^2+8t+c+8,则h(t)的图象与t轴有三个交点.
h'(t)=6t^2-16t+8=2(3t-2)(t-2)
h(t)的极大值h(2/3)=280/9+c,极小值是h(2)=8+c.
若h(t)的图象与t轴有三个交点,则h(2/3)=280/9+c>0且h(2)=8+c