导数是高考的重点考查知识,其中三次函数y=f(x)=ax~3+bx~2+cx+d(a,b,c,d∈R且a≠0)是一个重要模型.本文从三次函数的性质出发研究它的应用.1.三次函数的单调性性质1:当a>0且b~2-3ac≤0时,f(x)在(-∞,+∞)上单调递增;当a<0且b~2-3ac≤0时,f(x)在(-∞,+∞)上单调递减.性质2:若b~2-3ac>0,则f’(x)=0有两个解:x1= Derivatives are the key test knowledge of the college entrance examination, of which the cubic function y = f (x) = ax ~ 3 + bx ~ 2 + cx + d (a, b, c, d∈R and a ≠ 0) is an important model. Its application is studied from the nature of the cubic function.Formula of monotonicity of cubic function 1: f (x) increases monotonically (-∞, + ∞) when a> 0 and b ~ 2-3ac≤0 ; F (x) monotonously decreases over (-∞, + ∞) when a <0 and b ~ 2-3ac ≤ 0. Property 2: f ’(x) = 0 has two solutions: x1 =