第三章DISANZHANG导数应用

§1　函数的单调性与极值

1.1　导数与函数的单调性

课后训练案巩固提升

A组

1.函数y=xsin x+cos x在区间(　　)内是增函数,括号内为(　　)

A.(π/2 "," 3/2 π) B.(π,2π)

C.(3/2 π"," 5/2 π) D.(2π,3π)

解析:∵y'=sin x+xcos x-sin x=xcos x,∴当x∈(3/2 π"," 5/2 π)时,y'=xcos x>0.

答案:C

2.函数y=f(x)在定义域("-" 3/2 "," 3)内可导,其图像如图所示,记y=f(x)的导函数为y=f'(x),则不等式f'(x)≤0的解集为(　　)

A.["-" 1/3 "," 1]∪[2"," 3]

B.["-" 1"," 1/2]∪[4/3 "," 8/3]

C.["-" 3/2 "," 1/2]∪[1"," 2]

D.("-" 3/2 ",-" 1)∪[1/2 "," 4/3]∪[8/3 "," 3]