C.[kπ"-" 5π/12 "," kπ+π/12](k∈Z)

D.[kπ+π/12 "," kπ+7π/12](k∈Z)

(2)[2018·合肥一中月考] 已知ω>0,函数f(x)=cosωx+π/3在(π/3 "," π/2)上单调递增,则ω的取值范围是(　　)

A.(2/3 "," 10/3) B.[2/3 "," 10/3]

C.[2"," 10/3] D.(2"," 10/3)

[总结反思] (1)形如y=Asin(ωx+φ)的函数的单调性问题,一般是将ωx+φ看成一个整体,再结合图像利用y=sin x的单调性求解;(2)如果函数中自变量的系数为负值,要根据诱导公式把自变量系数化为正值,再确定其单调性.

应用演练

1.【微点3】[2018·西安八校联考] 已知函数f(x)=cos(x+θ)(0<θ<π)在x=π/3处取得最小值,则f(x)在[0,π]上的单调递增区间是 (　　)

A.[π/3 "," π] B.[π/3 "," 2π/3]

C.[0"," 2π/3] D.[2π/3 "," π]

2.【微点3】[2018·浙江余姚中学月考] 设f(x)=cos x,若a=f(ln 2),b=f(ln π),c=f(ln 1/3),则下列关系式正确的是 (　　)

A.a>b>c

B.b>c>a

C.a>c>b

D.b>a>c

3.【微点2】[2019·九江一中月考] 已知函数f(x)=Asin(ωx+π/6)的图像上相邻两个对称中心之间的距离为2,则函数的对称轴方程可能是 (　　)

A.x=1 B.x=1/4