函数零点是函数的重要性质,也是高考的热点,有些数学问题如能由题设的结构特征巧妙转化或构造出函数零点,往往使问题迎刃而解.现结合实例说明如下.一、巧化零点例1(2009年海南卷)已知函数f(x)=(x~3+3x~2+ax+b)e~(-x)(1)若a=b=-3,求f(x)的单调区间;(2)若f(x)在(-∞,α),(2,β)上单调递增,在(α,2),(β,+∞)上单调递减, Zero point is a function of the important nature of the function, but also a hot college entrance examination, and some mathematical problems such as the structural characteristics of the problem can be cleverly transformed or construct a function of zero, often solve the problem.Combined with examples are described below. (2009), we know that f (x) = (x ~ 3 + 3x ~ 2 + ax + b) e ~ (-x) (2) If f (x) monotonically increases on (-∞, α), (2, β) and monotonically decreases on (α, 2), (β, + ∞)