自 2 0 0 0年高考题给出关于“ｙ =-ｘｃｏｓｘ”的部分图象的选择题后 ,有关涉及两个单调函数乘积的单调性问题就受到中学数学界的普遍关注 .例如已知ｘ∈Ｒ ,ｆ(ｘ) =ｘ2 - 1 ,ｇ(ｘ) =ｘ ,试讨论Ｆ(ｘ) =ｆ(ｘ)ｇ(ｘ)的单调性 .对于此类问题 ,学生感到陌生 ,教师感到新颖 , Since the 2001 college entrance exam question gave a multiple-choice question about the partial image of “y =-xcosx”, the monotonicity problem involving the product of the two monotonic functions has received widespread attention from the middle school mathematics community. For example, known x ∈R ,f(x) =x2 - 1 ,g(x) =x, try to discuss the monotonicity of F(x) =f(x)g(x). For such problems, students are unfamiliar and teachers feel novel. ,