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#593c2f24-6aed-4c9d-94d7-e2dfb80760c3中等解答题导数压轴题常见模型导数及其应用

17.已知函数f(x)=2sinxxcosxxf(x)=2\sin x-x\cos x-xf(x)f\prime (x)f(x)f(x)的导数.
(1)求曲线y=f(x)y=f(x)在点A(0A(0f(0))f(0))处的切线方程;
(2)g(x)=x22x+a(aR)g(x)=x^{2}-2x+a(a\in R),若对任意x1[0x_{1}\in [0π]\pi ],均存在x2[1x_{2}\in [12]2],使得f(x1)>g(x2)f(x_{1})>g(x_{2}),求实数aa的取值范围.