Question

已知曲线C:y=x3 求过点(1,1)处的切线方程并求相应切线与曲线的交点坐标

Answer 1

y'=3x²

x=1 y'=3

切线方程：y=3(x-1)+1=3x-2

y=x^3

y=3x-2

联立得 x^3-3x+2=0

x^3-x-2x+2=0

x(x²-1)-2(x-1)=0

x(x-1)(x+1)-2(x-1)=0

(x-1)(x²+x-2)=0

(x-1)(x-1)(x+2)=0

x=1 or x=-2

交点(1,1) (-2,-8)