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在函数与导数的题目中,当涉及零点存在定理时,零点所在区间的端点值的找寻是学生学习的难点。在此,笔者归纳了以下几种方法来确定零点所在区间的端点值,与读者交流。1方法1:利用适当的因式分解或配方来寻找零点所在区间的端点值例1已知函数f(x)=x~2-(a+2)x+aln x+2a+2(a≤2)。(Ⅰ)求函数的单调区间;(Ⅱ)若函数在(0,2]上有且只有一个零点,求实数口的取值范围。
In the topic of functions and derivatives, when dealing with the existence theorem of zero point, finding the endpoint value of the interval where the zero locates is a difficult point for students to learn. Here, I summarize the following methods to determine the endpoint where the zero is located, and communicate with the reader. 1 Method 1: Finding the Endpoint Value of a Section Where the Zero Point Is Equated with an Appropriate Factorization or Recipe Example 1 Known Function f (x) = x ~ 2- (a + 2) x + aln x + 2a + 2 (a≤ 2). (Ⅰ) Find the monotone interval of the function; (Ⅱ) If the function has (0,2] and there is only one zero point, find the range of real numbers.