资源描述
2 2导数在实际问题中的应导数在实际问题中的应用用2 2.1 1实际问题中导数的意义MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1.理解平均变化率与导数的关系.2.理解导数的实际意义.3.体会导数的意义在实际生活中的应用.MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理生活中的变化率问题(1)在物理学中,通常称力在单位时间内做的功为功率,它的单位是瓦特.(2)在气象学中,通常把在单位时间(如1时、1天等)内的降雨量称作降雨强度,它是反映一次降雨大小的一个重要指标.(3)在经济学中,通常把生产成本y关于产量x的函数y=f(x)的导函数称为边际成本,边际成本f(x0)指的是当产量为x0时,生产成本的增加速度,也就是当产量为x0时,每增加一个单位的产量,需要增加f(x0)个单位的成本.MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理【变式训练】 假设某国家在20年间通货膨胀率为5%,物价p(单位:元)与时间t(单位:年)有如下函数关系:p(t)=p0(1+5%)t,其中p0为t=0时的物价.假定某种商品的p0=1,则在第10个年头,这种商品价格的上涨速度大约是多少?(精确到0.01元/年)解:因为p0=1,所以p(t)=(1+5%)t=1.05t.根据基本初等函数的导数公式,得p(t)=(1.05t)=1.05tln 1.05,所以p(10)=1.0510ln 1.050.08(元/年).故在第10个年头,这种商品价格的上涨速度约为0.08元/年.MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1 2 3 4 51如果质点A按规律s(t)=3t2运动,那么在t=3时的瞬时速度为()A.6B.18C.54 D.81解析:瞬时速度v(t)=s(t)=(3t2)=6t,v(3)=63=18.答案:BMUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1 2 3 4 5MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1 2 3 4 53做直线运动的某物体,其位移s与时间t的关系是s(t)=3t-t2,则该物体的初速度是.解析:s(t)=3-2t,s(0)=3,即该物体的初速度是3.答案:3MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1 2 3 4 54.竖直向上弹射一个小球,小球的初速度为100 m/s,试求小球何时的瞬时速度为0 m/s?(g9.8 m/s2,结果精确到0.1 s)MUBIAODAOHANG目标导航DIANLI TOUXI典例透析SUITANGYANLIAN随堂演练ZHISHI SHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理目标导航DIANLITOUXI典例透析SUITANGYANLIAN随堂演练ZHISHISHULI知识梳理1 2 3 4 55某企业每天的产品均能售出,售价为490元/吨,其每天的成本C与每天的产量q之间的函数关系为C(q)=2 000+450q+0.02q2.(1)写出收入函数;(2)写出利润函数;(3)求利润函数的导数,并说明其经济意义.解:设收入函数为R(q),利润函数为L(q).(1)收入函数为R(q)=490q.(2)利润函数为L(q)=R(q)-C(q)=490q-(2 000+450q+0.02q2)=-2 000+40q-0.02q2.(3)利润函数的导数为L(q)=(-2 000+40q-0.02q2)=40-0.04q.利润函数的导数称为边际利润,其经济意义为当产量达到q时,再增加单位产量后利润的改变量.
展开阅读全文