题1已知曲线C：f(x)=x~3-x+2,求经过点P(1,2)的曲线C的切线方程．学生的解答雷同：解由f′(x)=3x~2-1得切线的斜率k=f′(1)=2,所以过点P(1,2)的曲线C的切线方程为y-2=2(x-1),即y=2x．分析解题时犯了审题不清的错误．此处所求的切线只说经过P点,并没有说P点一定是切点．故切线的斜率k与f′(1)不一定相等． Problem 1 Known curve C:f(x)=x~3-x+2, find the tangent equation of curve C passing point P(1,2). The student’s solution is similar: the slope of the tangent from f′(x)=3x~2-1 is k=f′(1)=2, so the tangent equation of the curve C passing the point P(1,2) is y- 2=2(x-1), ie y=2x. Analytical problem-solving mistakes. The tangent line requested here only says to pass P point, and does not say P point must be tangent point. Therefore, the slope κ of the tangent line is not necessarily equal to f′(1).