函数与方程的思想反映了函数、方程、不等式之间的密切联系。对于函数y=f(x),令y=0,则转化为方程f(x)=0,函数值y的正负则转化为不等式f(x)>0或f(x)<0。由于导数的加入,让这三者间更密不可分。三者中函数是全局,方程、不等式是函数的局部。解决较复杂的问题时,不能只盯着局部,要从全局出发,函数、方程、不等式常常互相转化。在转化过程中不要忘记利用导数提供“动力”。下面借例题体会一下函数与方程的思想。 The ideas of function and equation reflect the close relationship between function, equation and inequality. For the function y = f (x), letting y = 0 translate to the equation f (x) = 0 and the positive and negative of the function y translate into the inequality f (x)> 0 or f (x) <0. Due to the addition of derivatives, let these three are more inseparable. The three functions are global, equations, inequalities are part of the function. To solve more complex problems, we can not just focus on the local situation. From a global perspective, functions, equations and inequalities often transform each other. Do not forget to use derivatives to provide “motivation ” during conversion. The following example to experience the function and equation ideas.