《高中数学 第三章 导数应用 3.1 函数的单调性与极值 3.1.2.1 函数的极值课件 北师大版选修22》由会员分享，可在线阅读，更多相关《高中数学 第三章 导数应用 3.1 函数的单调性与极值 3.1.2.1 函数的极值课件 北师大版选修22（30页珍藏版）》请在金锄头文库上搜索。
1、1 1.2 2函数的极值第1 1课时函数的极值ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1.
2、结合函数的图像,了解可导函数在某点处取得极值的必要条件和充分条件.2.理解函数极值的概念,理解函数的极值与导数的关系,会求函数的极值,并能确定是极大值还是极小值.3.增强学生数形结合的思维意识,提高学生运用导数的基本思想去分析和解决实际问题的能力.ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITA
3、NGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1.函数的极值的有关概念(1)在包含x0的一个区间(a,b)内,函数y=f(x)在任何一点的函数值都小于或等于x0点的函数值,称点x0为函数y=f(x)的极大值点,其函数值f(x0)为函数的极大值.在包含x0的一个区间(a,b)内,函数y=f(x)在任何一点的函数值都大于或等于x0点的函数值,称点x0为函数y=f(x)的极小值点,其函数值f(x0)为函数的极小值.极大值与极小值统称为极值,极大值点与
4、极小值点统称为极值点.ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航说明1.极值是一个局部性的概
5、念.由定义知,极值只是某个点的函数值与它附近点的函数值比较是最大或最小,并不意味着它在函数的整个定义域内最大或最小,即反映的是函数值在某一点附近的大小情况.2.函数的极值点一定出现在区间的内部,区间的端点不能成为极值点.3.函数的极值不是唯一的,即一个函数在某区间上的极大值或极小值可以不止一个.4.如果函数f(x)在a,b上有极值的话,那么它的极值点的分布是有规律的.相邻两个极大值点之间必有一个极小值点.同样,相邻两个极小值点之间必有一个极大值点.ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANG
6、YANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航5.极大值与极小值之间并无确定的大小关系,即一个函数的极大值未必大于极小值,如图所示,x1是极大值点,x4是极小值点,而f(x4)f(x1).ZHISHISHULI知识梳理SUITANGYANLIA
7、N随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航(2)如果函数y=f(x)在区间(a,x0)上是增加的,在区间(x0,b)上是减少的,那么x0是极大值点,
8、f(x0)是极大值.如果函数y=f(x)在区间(a,x0)上是减少的,在区间(x0,b)上是增加的,那么x0是极小值点,f(x0)是极小值.【做一做1】函数y=2-x2-x3的极值情况是()A.有极大值,没有极小值 B.有极小值,没有极大值C.既无极大值也无极小值D.既有极大值又有极小值答案:DZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析
9、目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航2.求函数极值点的步骤(1)求出导数f(x);(2)解方程f(x)=0;(3)对于方程f(x)=0的每一个解x0,分析f(x)在x0左、右两侧的符号(即f(x)的单调性),确定极值点;若f(x)在x0两侧的符号“左正右负”,则x0为极大值点;若f(x)在x0两侧的符号“左负右正”,则x0为极小值点;若f(x)在x0两侧的符号相同,则x0不是极值点.ZH
10、ISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航说明导数值为0的点不一定是函数的极值点.例如,对于函数
11、f(x)=x3,我们有f(x)=3x2.显然f(0)=0,但无论x0,还是x0,所以x=0不是函数f(x)=x3的极值点.一般地,“函数y=f(x)在一点处的导数存在,且导数值为0”是“函数y=f(x)在这点处取得极值”的必要不充分条件.ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYAN
12、LIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航A.2B.2,-1 C.-1 D.-3解析:f(x)=-x2+x+2,令f(x)=0,即-x2+x+2=0,解得x1=-1,x2=2.当x2时,f(x)0,f(x)在(-,-1),(2,+)上是减少的;当-1x0,f(x)在(-1,2)上是增加的.故x=-1是函数的极小值点.答案:CZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知
13、识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIA
14、N随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI
15、典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三反思反思1.极大值不一定比极小值大,这是因为极值是相对某一区间而言的;2.借助函数的性质(如奇偶性、单调性、极值、周期等)研究函数图像是重要手段.ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLI
16、TOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHI
17、SHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUIT
18、ANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三【例2】已知f(x)=ax3+bx2+cx(a0)在x=1处取得极值,且f(1)=-1.(1)试求常数a,b,c的值;(2)试判断x=1是函数的极大值点还是极小值点,并说明理
19、由.ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三ZHISHISHULI知识梳
20、理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三ZHISHISHULI知识梳理SUITANGYANLIAN随
21、堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三(2)x=-1是极大值点,x=1是极小值点.理由如下:当x1时,f(x)0,当-1x1时,f
22、(x)0.故当x=1时,f(x)取得极小值.当a=-3,b=3时,f(x)=3(x-1)20,即x=1不是极值点.所以舍去a=-3,b=3.故a+b=-7.ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识
23、梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 51关于函数的极值,下列说法正确的是()A.导数为零的点一定是函数的极值点B.函数的极小值一定小于它的极大值C.f(x)在定义域内最多只能有一个极大值和一个极小值D.如果f(x)在(a,b)内有极值,那么f(x)在(a,b)内不是单调函数解析:导数为零的点不一定是极值点,如f(x)=x3,f(0)=0,但x=0不是极值点.极小值不一定小于极大值.f(x)在定义域内可能有多个极值点.答案:D6ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOU
24、XI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 52若函数f(x)=xex,则()A.x=1为f(x)的极大值点B.x=-1为f(x)的极大值点C.x=1为f(x)的
25、极小值点D.x=-1为f(x)的极小值点答案:D6ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHISHULI知识梳理SUITANGYANLIAN随堂演练DIANLITOUXI典例透析目标导航ZHISHI SHULI知识梳理SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 53已知f(x)=x3+ax2+(a+6)x+1有极大值和极小值,则a的取值范围为()A.-1a2B.-3a6C.a2D.a6解析:f(x)=3x2+2ax+a+6,因为f(x)既有极大值又有极小值,所以=(2a)2-43(a+6)0,解得a6或a0,解得a1.故a的取值范围为(-,1).
