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一.内容和内容解析
本节内容有函数零点概念、函数零点与相应方程根的关系、函数零点存在性定理.
函数零点是研究当函数的值为零时,相应的自变量的取值,反映在函数图象上,也就是函数图象与轴的交点横坐标.
由于函数的值为零亦即,其本身已是方程的形式,因而函数的零点必然与方程有着不可分割的联系,事实上,若方程有解,则函数存在零点,且方程的根就是相应函数的零点,也是函数图象与轴的交点横坐标.顺理成章的,方程的求解问题,可以转化为求函数零点的问题.这是函数与方程关系认识的第一步.
零点存在性定理,是函数在某区间上存在零点的充分不必要条件.如果函数在区间[a,b]上的图象是一条连续不断的曲线,并且满足f(a)·f(b)
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