巧构辅助函数解决微分中值定理相关习题

Cleverly Constructing Auxiliary Functions to Solve Related Exercises of Differential Mean Value Theorem

使用不定积分学习微积分中值定理相关习题时,我们既可以把需要构造导函数的原函数理解为是多个初等函数的和差,也可以理解为是多个函数乘积的导数。另外,考虑到微分中值定理学习过程中不定积分的重要性,我们建议在学习微积分的时候采取如下的学习顺序:导数→不定积分→微分中值定理。

Using indefinite integrals to solve exercises related to differential mean value theorem,we can understand that the structured original function of the derivative is the sum and difference of some elementary functions and also understand that it is the product of several functions.So,in view of the importance of the derivative and indefinite integrals in learning differential mean value theorem,we recommend the following sequence of learning when learning calculus：derivative→rindefinite integrals→differential mean value theorem.