曲线y=x3-3x2+1在点(2,-3)处的切线方程为(  ) A.y=-3x+3 B.y=-3x+1 C.y=-3 D.x=2

问题描述:

曲线y=x3-3x2+1在点(2,-3)处的切线方程为(  )
A. y=-3x+3
B. y=-3x+1
C. y=-3
D. x=2

∵y=x3-3x2+1,
∴y′=3x2-6x,
∵f′(2)=12-12=0,
∴曲线y=x3-3x2+1在点(2,-3)处的切线方程为:
y+3=0×(x-2),即y+3=0.
故选::C.