高中數(shù)學(xué) 第三章 導(dǎo)數(shù)應(yīng)用 3.1 函數(shù)的單調(diào)性與極值 3.1.2.1 函數(shù)的極值課件 北師大版選修22

《高中數(shù)學(xué) 第三章 導(dǎo)數(shù)應(yīng)用 3.1 函數(shù)的單調(diào)性與極值 3.1.2.1 函數(shù)的極值課件 北師大版選修22》由會(huì)員分享，可在線閱讀，更多相關(guān)《高中數(shù)學(xué) 第三章 導(dǎo)數(shù)應(yīng)用 3.1 函數(shù)的單調(diào)性與極值 3.1.2.1 函數(shù)的極值課件 北師大版選修22（30頁珍藏版）》請?jiān)谘b配圖網(wǎng)上搜索。

1、1 1.2 2函數(shù)的極值第1 1課時(shí)函數(shù)的極值MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1.

2、結(jié)合函數(shù)的圖像,了解可導(dǎo)函數(shù)在某點(diǎn)處取得極值的必要條件和充分條件.2.理解函數(shù)極值的概念,理解函數(shù)的極值與導(dǎo)數(shù)的關(guān)系,會(huì)求函數(shù)的極值,并能確定是極大值還是極小值.3.增強(qiáng)學(xué)生數(shù)形結(jié)合的思維意識,提高學(xué)生運(yùn)用導(dǎo)數(shù)的基本思想去分析和解決實(shí)際問題的能力.MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航D

3、IANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1.函數(shù)的極值的有關(guān)概念(1)在包含x0的一個(gè)區(qū)間(a,b)內(nèi),函數(shù)y=f(x)在任何一點(diǎn)的函數(shù)值都小于或等于x0點(diǎn)的函數(shù)值,稱點(diǎn)x0為函數(shù)y=f(x)的極大值點(diǎn),其函數(shù)值f(x0)為函數(shù)的極大值.在包含x0的一個(gè)區(qū)間(a,b)內(nèi),函數(shù)y=f(x)在任何一點(diǎn)的函數(shù)值都大于或等于x0點(diǎn)的函數(shù)值,稱點(diǎn)x0為函數(shù)y=f(x)的極小值點(diǎn),其函數(shù)值f(x0)為函數(shù)的極小值.極大值與極小值統(tǒng)稱為極值,極大值點(diǎn)與

4、極小值點(diǎn)統(tǒng)稱為極值點(diǎn).MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理說明1.極值是一個(gè)局部性的概

5、念.由定義知,極值只是某個(gè)點(diǎn)的函數(shù)值與它附近點(diǎn)的函數(shù)值比較是最大或最小,并不意味著它在函數(shù)的整個(gè)定義域內(nèi)最大或最小,即反映的是函數(shù)值在某一點(diǎn)附近的大小情況.2.函數(shù)的極值點(diǎn)一定出現(xiàn)在區(qū)間的內(nèi)部,區(qū)間的端點(diǎn)不能成為極值點(diǎn).3.函數(shù)的極值不是唯一的,即一個(gè)函數(shù)在某區(qū)間上的極大值或極小值可以不止一個(gè).4.如果函數(shù)f(x)在a,b上有極值的話,那么它的極值點(diǎn)的分布是有規(guī)律的.相鄰兩個(gè)極大值點(diǎn)之間必有一個(gè)極小值點(diǎn).同樣,相鄰兩個(gè)極小值點(diǎn)之間必有一個(gè)極大值點(diǎn).MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIA

6、NLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理5.極大值與極小值之間并無確定的大小關(guān)系,即一個(gè)函數(shù)的極大值未必大于極小值,如圖所示,x1是極大值點(diǎn),x4是極小值點(diǎn),而f(x4)f(x1).MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUX

7、I典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理(2)如果函數(shù)y=f(x)在區(qū)間(a,x0)上是增加的,在區(qū)間(x0,b)上是減少的,那么x0是極大值點(diǎn),

8、f(x0)是極大值.如果函數(shù)y=f(x)在區(qū)間(a,x0)上是減少的,在區(qū)間(x0,b)上是增加的,那么x0是極小值點(diǎn),f(x0)是極小值.【做一做1】 函數(shù)y=2-x2-x3的極值情況是()A.有極大值,沒有極小值 B.有極小值,沒有極大值C.既無極大值也無極小值D.既有極大值又有極小值答案:DMUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIA

9、N隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理2.求函數(shù)極值點(diǎn)的步驟(1)求出導(dǎo)數(shù)f(x);(2)解方程f(x)=0;(3)對于方程f(x)=0的每一個(gè)解x0,分析f(x)在x0左、右兩側(cè)的符號(即f(x)的單調(diào)性),確定極值點(diǎn);若f(x)在x0兩側(cè)的符號“左正右負(fù)”,則x0為極大值點(diǎn);若f(x)在x0兩側(cè)的符號“左負(fù)右正”,則x0為極小值點(diǎn);若f(x)在x0兩側(cè)的符號相同,則x0不是極值點(diǎn).M

10、UBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理說明導(dǎo)數(shù)值為0的點(diǎn)不一定是函數(shù)的極值點(diǎn).例如,對于函

11、數(shù)f(x)=x3,我們有f(x)=3x2.顯然f(0)=0,但無論x0,還是x0,所以x=0不是函數(shù)f(x)=x3的極值點(diǎn).一般地,“函數(shù)y=f(x)在一點(diǎn)處的導(dǎo)數(shù)存在,且導(dǎo)數(shù)值為0”是“函數(shù)y=f(x)在這點(diǎn)處取得極值”的必要不充分條件.MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANL

12、ITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理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.當(dāng)x2時(shí),f(x)0,f(x)在(-,-1),(2,+)上是減少的;當(dāng)-1x0,f(x)在(-1,2)上是增加的.故x=-1是函數(shù)的極小值點(diǎn).答案:CMUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI

13、知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITO

14、UXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYA

15、NLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三反思反思1.極大值不一定比極小值大,這是因?yàn)闃O值是相對某一區(qū)間而言的;2.借助函數(shù)的性質(zhì)(如奇偶性、單調(diào)性、極值、周期等)研究函數(shù)圖像是重要手段.MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITA

16、NGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHI

17、SHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)

18、航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三【例2】 已知f(x)=ax3+bx2+cx(a0)在x=1處取得極值,且f(1)=-1.(1)試求常數(shù)a,b,c的值;(2)試判斷x=1是函數(shù)的極大值點(diǎn)還是極小值點(diǎn),并說

19、明理由.MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三MUBIAODAOHAN

20、G目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUX

21、I典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理題型一題型二題型三(2)x=-1是極大值點(diǎn),x=1是極小值點(diǎn).理由如下:當(dāng)x1時(shí),f(x)0,當(dāng)-1x1時(shí)

22、,f(x)0.故當(dāng)x=1時(shí),f(x)取得極小值.當(dāng)a=-3,b=3時(shí),f(x)=3(x-1)20,即x=1不是極值點(diǎn).所以舍去a=-3,b=3.故a+b=-7.MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知

23、識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1 2 3 4 51關(guān)于函數(shù)的極值,下列說法正確的是()A.導(dǎo)數(shù)為零的點(diǎn)一定是函數(shù)的極值點(diǎn)B.函數(shù)的極小值一定小于它的極大值C.f(x)在定義域內(nèi)最多只能有一個(gè)極大值和一個(gè)極小值D.如果f(x)在(a,b)內(nèi)有極值,那么f(x)在(a,b)內(nèi)不是單調(diào)函數(shù)解析:導(dǎo)數(shù)為零的點(diǎn)不一定是極值點(diǎn),如f(x)=x3,f(0)=0,但x=0不是極值點(diǎn).極小值不一定小于極大值.f(x)在定義域內(nèi)可能有多個(gè)極值點(diǎn).答案:D6MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANG

24、YANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1 2 3 4 52若函數(shù)f(x)=xex,則()A.x=1為f(x)的極大值點(diǎn)B.x=-1為f(x)的極大值點(diǎn)C.x=1為f(x

25、)的極小值點(diǎn)D.x=-1為f(x)的極小值點(diǎn)答案:D6MUBIAODAOHANG目標(biāo)導(dǎo)航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標(biāo)導(dǎo)航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1 2 3 4 53已知f(x)=x3+ax2+(a+6)x+1有極大值和極小值,則a的取值范圍為()A.-1a2B.-3a6C.a2D.a6解析:f(x)=3x2+2ax+a+6,因?yàn)閒(x)既有極大值又有極小值,所以=(2a)2-43(a+6)0,解得a6或a0,解得a1.故a的取值范圍為(-,1).