若函数f(x)=2asinxcosx-a*(根号2)*(sinx+cosx)+a+b的定义域为[0,派/2],值域为[-
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若函数f(x)=2asinxcosx-a*(根号2)*(sinx+cosx)+a+b的定义域为[0,派/2],值域为[-5,1],求a,b的值
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![若函数f(x)=2asinxcosx-a*(根号2)*(sinx+cosx)+a+b的定义域为[0,派/2],值域为[-](/uploads/image/z/5463974-38-4.jpg?t=%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%3D2asinxcosx-a%2A%28%E6%A0%B9%E5%8F%B72%29%2A%28sinx%2Bcosx%29%2Ba%2Bb%E7%9A%84%E5%AE%9A%E4%B9%89%E5%9F%9F%E4%B8%BA%5B0%2C%E6%B4%BE%2F2%5D%2C%E5%80%BC%E5%9F%9F%E4%B8%BA%5B-)
f'(x)=2a[cos2x-cos(x+派/4)]
令f'(x)=0 =〉
x=派/4
又 f(0)=(1-根号2)a+b
=f(派/2)=(1-根号2)a+b
所以f(派/4)=1 f(0)=-5
或f(派/4)=-5 f(0)=1
解之a=6根号2+6 b=1
或a=--6根号2-6 b=-5
令f'(x)=0 =〉
x=派/4
又 f(0)=(1-根号2)a+b
=f(派/2)=(1-根号2)a+b
所以f(派/4)=1 f(0)=-5
或f(派/4)=-5 f(0)=1
解之a=6根号2+6 b=1
或a=--6根号2-6 b=-5
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