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导数是一个特殊函数,它的引出和定义始终贯穿着函数思想。所以导数问题即为研究函数问题。本文将通过具体实例揭示运用导数解决函数的单调性、极值以及最值问题的本质。关键在于判断f′(x)的正负,当f′(x)>0时,f(x)单调递增;当f′(x)<0时,f(x)单调递减,进而求出函数的极值与最值,所以三者的研究方法和谐统一。1问题本质实际上导数与我们前面所学的知识有着千丝万缕的联系。先看下面一个例子:
Derivative is a special function, its derivation and definition always runs through the function of thought. So the problem of the derivative is to study the function problem. In this paper, the monotonicity, extremum and the essence of the most value problem of solving a function are revealed through concrete examples. The key point is to judge the positive and negative of f ’(x), f (x) monotonically increases when f’ (x)> 0, and monotonically decreases f (x) <0, The extreme value and the most value, so the three research methods are harmoniously unified. The Nature of the Problem In fact, the derivative is inextricably linked to the knowledge we have learned before. Take a look at an example below: