上高三复习课时,我讲解了2007年全国卷Ⅱ第22题,不料,变成了一节研究性学习课,现将它奉献给大家,希望对广大读者有所启示和帮助.1原题再现已知函数f(x)=x3-x.(1)求曲线y=f(x)在点M(t,f(t))处的切线方程;(2)设a0,如果过点(a,b)可作曲线y=f(x)的三条切线,证明:-abf(a).解(1)解 When I was in the high school reviewing class, I explained the 22th issue of the 2007 National Volume II. Unexpectedly, I turned it into a research-based learning class, and I hereby dedicate it to all of you. I hope this book will provide some inspiration and help to our readers. (1) Find the tangent equation of curve y = f (x) at point M (t, f (t)); (2) Suppose a0, , b) Make three tangents to the curve y = f (x), proving: -abf (a). Solution (1) Solution