已知函数f(x)=-2a sin(2x+π/6)+a+b的定义域为【0,π/2】,值域为【-5,4】,求常数a、b的值.-1/2

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已知函数f(x)=-2a sin(2x+π/6)+a+b的定义域为【0,π/2】,值域为【-5,4】,求常数a、b的值.-1/2
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已知函数f(x)=-2a sin(2x+π/6)+a+b的定义域为【0,π/2】,值域为【-5,4】,求常数a、b的值.-1/2
已知函数f(x)=-2a sin(2x+π/6)+a+b的定义域为【0,π/2】,值域为【-5,4】,求常数a、b的值.
-1/2

已知函数f(x)=-2a sin(2x+π/6)+a+b的定义域为【0,π/2】,值域为【-5,4】,求常数a、b的值.-1/2
分情况讨论a>0和 a

0π/6<2x+π/6<7π/6
2x+π/6=π/2
sin(2x+π/6)=1
2x+π/6=7π/6
sin(2x+π/6)=-1/2
1)a>0
f(x)max=3a+b=4
f(x)min=-a+b=-5
a=9/4 b=-11/4
2)a<0
f(x)max=-a+b=4
f(x)min=3a+b=-5
a=-9/4 b=7/4