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用导数法求函数的极值,是求极值基本方法,在解决这类问题时,如果对法则、定理一知半解或理解不透,很容易造成极值点的遗漏.可导函数y=f(x)在某一点x_0处取得极值的必要条件是这一点x_0的导数f′(x_0)=0.因此求可导函数y=f(x)的极值可以按照下列步骤进行: ①先求函数y=f(x)的导数f′(x); ②令f′(x)=0求得根x_0; ③在x_0附近左右两侧判断f′(x_0)的符号,左正右负为极大值点,左负右正为极小值点.
The use of derivative method to find the extremum of a function is the basic method of extremum. When solving such problems, if the law or theorem is partially understood or understood, it is easy to cause the omission of extreme points. The derivative function y=f ( x) The necessary condition for obtaining the extremum at a certain point x_0 is that the derivative of this point x_0 is f′(x_0)=0. Therefore, finding the extremum of the derivative function y=f(x) can be performed according to the following steps: The function y=f(x)’s derivative f’(x); 2 Let f’(x)=0 get the root x_0; 3 Determine the sign of f’(x_0) in the left and right sides of x_0, left plus right and minus The maximum point, left-right negative is the minimum point.