《高中數(shù)學 第三章 導數(shù)應用 3.2導數(shù)在實際問題中的應用 3.2.1 實際問題中導數(shù)的意義課件 北師大版選修22》由會員分享，可在線閱讀，更多相關《高中數(shù)學 第三章 導數(shù)應用 3.2導數(shù)在實際問題中的應用 3.2.1 實際問題中導數(shù)的意義課件 北師大版選修22（12頁珍藏版）》請在裝配圖網上搜索。

1、2 2導數(shù)在實際問題中的應導數(shù)在實際問題中的應用用2 2.1 1實際問題中導數(shù)的意義MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂

2、演練ZHISHISHULI知識梳理1.理解平均變化率與導數(shù)的關系.2.理解導數(shù)的實際意義.3.體會導數(shù)的意義在實際生活中的應用.MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOU

3、XI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理生活中的變化率問題(1)在物理學中,通常稱力在單位時間內做的功為功率,它的單位是瓦特.(2)在氣象學中,通常把在單位時間(如1時、1天等)內的降雨量稱作降雨強度,它是反映一次降雨大小的一個重要指標.(3)在經濟學中,通常把生產成本y關于產量x的函數(shù)y=f(x)的導函數(shù)稱為邊際成本,邊際成本f(x0)指的是當產量為x0時,生產成本的增加速度,也就是當產量為x0時,每增加一個單位的產量,需要增加f(x0)個單位的成本.MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練Z

4、HISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLI

5、TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂

6、演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理【變式訓練】 假設某國家在20年間通貨膨脹率為5%,物價p(單位:元)與時間t(單位:年)有如下函數(shù)關系:p(t)=p0(1+5%)t,其中p0為t=0時的物價.假定某種商品的p0=1,則在第10個年頭,這種商品價格的上漲速度大約是多少?(精確到0.01

7、元/年)解:因為p0=1,所以p(t)=(1+5%)t=1.05t.根據(jù)基本初等函數(shù)的導數(shù)公式,得p(t)=(1.05t)=1.05tln 1.05,所以p(10)=1.0510ln 1.050.08(元/年).故在第10個年頭,這種商品價格的上漲速度約為0.08元/年.MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISH

8、ULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1 2 3 4 51如果質點A按規(guī)律s(t)=3t2運動,那么在t=3時的瞬時速度為()A.6B.18C.54 D.81解析:瞬時速度v(t)=s(t)=(3t2)=6t,v(3)=63=18.答案:BMUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SU

9、ITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1 2 3 4 5MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練

10、ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1 2 3 4 53做直線運動的某物體,其位移s與時間t的關系是s(t)=3t-t2,則該物體的初速度是.解析:s(t)=3-2t,s(0)=3,即該物體的初速度是3.答案:3MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGY

11、ANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1 2 3 4 54.豎直向上彈射一個小球,小球的初速度為100 m/s,試求小球何時的瞬時速度為0 m/s?(g9.8 m/s2,

12、結果精確到0.1 s)MUBIAODAOHANG目標導航DIANLI TOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHI SHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理目標導航DIANLITOUXI典例透析SUITANGYANLIAN隨堂演練ZHISHISHULI知識梳理1 2 3 4 55某企業(yè)每

13、天的產品均能售出,售價為490元/噸,其每天的成本C與每天的產量q之間的函數(shù)關系為C(q)=2 000+450q+0.02q2.(1)寫出收入函數(shù);(2)寫出利潤函數(shù);(3)求利潤函數(shù)的導數(shù),并說明其經濟意義.解:設收入函數(shù)為R(q),利潤函數(shù)為L(q).(1)收入函數(shù)為R(q)=490q.(2)利潤函數(shù)為L(q)=R(q)-C(q)=490q-(2 000+450q+0.02q2)=-2 000+40q-0.02q2.(3)利潤函數(shù)的導數(shù)為L(q)=(-2 000+40q-0.02q2)=40-0.04q.利潤函數(shù)的導數(shù)稱為邊際利潤,其經濟意義為當產量達到q時,再增加單位產量后利潤的改變量.