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1.缘起大家知道,三次函数f(x)=ax~3+bx~2+cx+d,(a,b,c,d∈R,a≠0)作为导数运用的一个基本载体,平时的训练主要侧重于单调性、极值或最值、零点、切线等问题,而关于函数的几何特征—图像的对称性并没有进行较深入的研究(仅限于勾画一些函数的草图).这就导致了学生遇到一些特殊问题时,就会茫然无措.在高三复习训练中,笔者就曾经给学生布置过以下两道小题:
1. From the origin we all know that the third order function f (x) = ax ~ 3 + bx ~ 2 + cx + d, (a, b, c, d∈R, a ≠ 0) Training mainly focuses on monotonicity, extreme value or maximum value, zero point, tangent and other issues, and the geometric features of the function - the symmetry of the image has not been studied in more depth (sketching only the sketches of some functions) The students encountered some special problems, will be at a loss.In the third year of senior high school review training, I had arranged for students to have the following two small problems: