2019-2020学年人教B版选修2-2 7 导数的实际应用 作业(1)
2019-2020学年人教B版选修2-2 7 导数的实际应用 作业(1)第1页

1.3.3 导数的实际应用

1以长为10的线段AB为直径画半圆,则它的内接矩形面积的最大值为(  )

                

A.10 B.15 C.25 D.50

答案:C

2某公司生产某种产品,固定成本为20 000元,每生产一件产品,成本增加100元,已知总收益R(单位:元)与年产量x(单位:件)的关系是R={■(400x"-" 1/2 x^2 "," 0≤x≤400"," @80" " 000"," x>400"," )┤则当总利润P最大时,每年的产量是(  )

A.100件 B.150件

C.200件 D.300件

解析:由题意,总成本为C=20 000+100x.

  所以总利润P=R-C

  ={■(400x"-" 1/2 x^2 "-" 100x"-" 20" " 000"," 0≤x≤400"," @80" " 000"-" 100x"-" 20" " 000"," x>400"," )┤

  则P'={■(300"-" x"," 0≤x≤400"," @"-" 100"," x>400"," )┤

  令P'=0,得x=300,

  易知当x=300(件)时,总利润最大.

答案:D

3要做一个圆锥形的漏斗,其母线长为20 cm,要使其体积最大,则高为(  )

A.√3/3 cmB.(10√3)/3 cm