独立学院数学改革之数学实验——Matlab平台上“四步法”研究函数的单调性与凹凸性

数学实验是高等数学改革的重要方向,借助数学软件简化数学计算,注重数学应用是数学教学的一个新动向。函数的单调性与凹凸性是高等数学中导数应用部分的一个重要内容。本文借助功能强大的数学软件Matlab,巧用计算与图形功能,提出应用导数研究函数的单调性与凹凸性的四步法,即(1)求导函数;(2)求导函数的零点;(3)画原函数与导函数图;(4)确定函数的单调性或凹凸性。该方法采用先求导函数零点再画图的顺序,确保画图区域包含导函数的零点,避免遗漏极值点或拐点,进一步通过实例系统体现该方法对函数单调性与凹凸性的可视化判定。

Mathematical Experiment in Mathematics Reform in Independent College:"Four Steps"Researches Function Monotonicity and Cancave-conves Effects Based on Matlab

Function monotonicity and concave-conves effects are important contents of derivative application part in higher mathematics. With the help of Matlab which is a powerful mathematical software system, this paper by using Matlab calculation and graphics functions, proposes the four steps to research function monotonicity and concave-conves effects, namely（1） the derivation function;（2） the roots of derivative function;（3） draw function and the derived function;（4） determine the monotonicity or concave-conves effects. The method calculates the roots of derivative function then draws and the drawing area contains roots of derivative function, which can avoid the omission of extreme points or inflection points; furthermore, the examples demonstrate the method for function monotonicity and concaveconves effects visual judgment.