y=x³-3x²+2x
对x求导,得y'=3x²-6x+2
由题意,得
3(x0)²-6(x0)+2=k……①
(x0)³-3(x0)²+2(x0)=k(x0)……②
(1)若x0=0,则k=2成立
(2)若x0≠0,则由②,得(x0)²-3(x0)+2=k……③
将①代入③,得
(x0)²-3(x0)+2=3(x0)²-6(x0)+2
2(x0)²-3(x0)=0
2(x0)=3
x0=3/2
此时k=(9/4)-3*(3/2)+2=-1/4
综上,直线l为y=2x 或y=(-1/4)x
切点分别为(0,0)和(3/2,-3/8)
完毕!