已知\(f(x) = 2\sqrt 3 \sin \omega x\cos \omega x + 2{\cos ^2}\omega x(\o-可可试卷app

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已知 \(f(x) = 2\sqrt 3 \sin \omega x\cos \omega x + 2{\cos ^2}\omega x(\omega > 0)\) ，若函数在区间 \((\frac{\pi }{2},\pi )\) 内不存在对称轴，则 \(\omega \) 的取值范围为( )

A.\((0，\frac {1} {6}]\cup \left [ {\frac {1} {3}，\frac {3} {4}} \right ]\)

B.\((0，\frac {1} {3}]\cup \left [ {\frac {2} {3}，\frac {3} {4}} \right ]\)

C.\((0，\frac {1} {6}]\cup \left [ {\frac {1} {3}，\frac {2} {3}} \right ]\)

D.\((0，\frac {1} {3}]\cup \left [ {\frac {2} {3}，\frac {5} {6}} \right ]\)

参考答案：C