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
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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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