y=x³-3x²+2x
對(duì)x求導(dǎo),得y'=3x²-6x+2
由題意,得
3(x0)²-6(x0)+2=k……①
(x0)³-3(x0)²+2(x0)=k(x0)……②
(1)若x0=0,則k=2成立
(2)若x0≠0,則由②,得(x0)²-3(x0)+2=k……③
將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
此時(shí)k=(9/4)-3*(3/2)+2=-1/4
綜上,直線l為y=2x 或y=(-1/4)x
切點(diǎn)分別為(0,0)和(3/2,-3/8)
完畢!