已知函数f(x)=asinx+bx的图像在点(π/3,f(π/3))处的切线方程x+2y-根号3+π/3=0(1)求实数a,b的值 (2)当0<x<π/2时,f(X)>(m-1)x恒成立,求实数m的取值范围
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![已知函数f(x)=asinx+bx的图像在点(π/3,f(π/3))处的切线方程x+2y-根号3+π/3=0(1)求实数a,b的值 (2)当0<x<π/2时,f(X)>(m-1)x恒成立,求实数m的取值范围](/uploads/image/z/6951210-42-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dasinx%2Bbx%E7%9A%84%E5%9B%BE%E5%83%8F%E5%9C%A8%E7%82%B9%28%CF%80%2F3%2Cf%28%CF%80%2F3%29%29%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8Bx%2B2y-%E6%A0%B9%E5%8F%B73%2B%CF%80%2F3%3D0%281%29%E6%B1%82%E5%AE%9E%E6%95%B0a%2Cb%E7%9A%84%E5%80%BC+%EF%BC%882%EF%BC%89%E5%BD%930%EF%BC%9Cx%EF%BC%9C%CF%80%2F2%E6%97%B6%2Cf%28X%29%EF%BC%9E%28m-1%29x%E6%81%92%E6%88%90%E7%AB%8B%2C%E6%B1%82%E5%AE%9E%E6%95%B0m%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
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已知函数f(x)=asinx+bx的图像在点(π/3,f(π/3))处的切线方程x+2y-根号3+π/3=0(1)求实数a,b的值 (2)当0<x<π/2时,f(X)>(m-1)x恒成立,求实数m的取值范围
已知函数f(x)=asinx+bx的图像在点(π/3,f(π/3))处的切线方程x+2y-根号3+π/3=0
(1)求实数a,b的值 (2)当0<x<π/2时,f(X)>(m-1)x恒成立,求实数m的取值范围
已知函数f(x)=asinx+bx的图像在点(π/3,f(π/3))处的切线方程x+2y-根号3+π/3=0(1)求实数a,b的值 (2)当0<x<π/2时,f(X)>(m-1)x恒成立,求实数m的取值范围
切线方程变形为 y=(-1/2)(x-1) 1
可见斜率k=-1/2, f(1)=1
f'(x)=[a(x 1)/x-alnx]/(x 1)^2-b/x^2
已知k=f'(1)=(2a)/4-b=-1/2 即a-2b=-1 (1)
f(1)=b=1
代入(1)得 a=1
(2) x>0时
f(x)-lnx/(x 1)=1/x>0
得证
求导,不难