已知a>0,函数f(x)=-a(2cos²x+√3 sin2x)+3a+b,当x∈[0,π/2]时,-5≤f(x)≤1.(1)求常数a,b的值.(2)设g(x)=f(x+π/2),且lg[g(x)]>0,求g(x)的单调递增区间.
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已知a>0,函数f(x)=-a(2cos²x+√3 sin2x)+3a+b,当x∈[0,π/2]时,-5≤f(x)≤1.(1)求常数a,b的值.(2)设g(x)=f(x+π/2),且lg[g(x)]>0,求g(x)的单调递增区间.
已知a>0,函数f(x)=-a(2cos²x+√3 sin2x)+3a+b,当x∈[0,π/2]时,-5≤f(x)≤1.
(1)求常数a,b的值.
(2)设g(x)=f(x+π/2),且lg[g(x)]>0,求g(x)的单调递增区间.
已知a>0,函数f(x)=-a(2cos²x+√3 sin2x)+3a+b,当x∈[0,π/2]时,-5≤f(x)≤1.(1)求常数a,b的值.(2)设g(x)=f(x+π/2),且lg[g(x)]>0,求g(x)的单调递增区间.
f(x)=-a(2cos²x+√3 sin2x)+3a+b
=-a(cso2x+√3sin2x)+4a+b
=-a/2·sin(2x+π/6)+4a+b
x∈[0,π/2] ,
2x+π/6∈[π/6,7π/6]
sin(2x+π/6)∈[-1/2,1]
f(x)∈[15a/4+b,7a/2+b] -5≤f(x)≤1
所以15a/4+b=-5,7a/2+b=1
a=-16,b=57
(1)f(x)=-a(cos2x+√3sin2x+1)+3a+b=-2asin(2x+π/6)+3a+b
当x∈[0,π/2]时,2x+π/6∈[π/6,7π/6],sin(2x+π/6)∈[-1/2,1]
又∵a>0∴1/2a+3a+b=1,-a+3a+b=-5→a=4,b=-13
(2)f(x)=-4sin(2x+π/6)-1,g(x)=-4sin(2x+π+π/6)-...
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(1)f(x)=-a(cos2x+√3sin2x+1)+3a+b=-2asin(2x+π/6)+3a+b
当x∈[0,π/2]时,2x+π/6∈[π/6,7π/6],sin(2x+π/6)∈[-1/2,1]
又∵a>0∴1/2a+3a+b=1,-a+3a+b=-5→a=4,b=-13
(2)f(x)=-4sin(2x+π/6)-1,g(x)=-4sin(2x+π+π/6)-1=4sin(2x+π/6)-1
∴g(x)的单调递增区间为[-π/3+kπ,π/6+kπ],k∈N*
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