f(x)=2cos^x+根号3sin2x+a,(1)若x属于R,求f(x)的递增区间f(x)=2cos^x+根号3*sin2x+a,(1)若x属于R,求f(x)的递增区间(2)当x属于[0,pai/2]时,f(x)
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![f(x)=2cos^x+根号3sin2x+a,(1)若x属于R,求f(x)的递增区间f(x)=2cos^x+根号3*sin2x+a,(1)若x属于R,求f(x)的递增区间(2)当x属于[0,pai/2]时,f(x)](/uploads/image/z/10298829-21-9.jpg?t=f%28x%29%3D2cos%5Ex%2B%E6%A0%B9%E5%8F%B73sin2x%2Ba%2C%281%29%E8%8B%A5x%E5%B1%9E%E4%BA%8ER%2C%E6%B1%82f%28x%29%E7%9A%84%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4f%28x%29%3D2cos%5Ex%2B%E6%A0%B9%E5%8F%B73%2Asin2x%2Ba%2C%281%29%E8%8B%A5x%E5%B1%9E%E4%BA%8ER%2C%E6%B1%82f%28x%29%E7%9A%84%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4%282%29%E5%BD%93x%E5%B1%9E%E4%BA%8E%5B0%2Cpai%2F2%5D%E6%97%B6%2Cf%28x%29)
f(x)=2cos^x+根号3sin2x+a,(1)若x属于R,求f(x)的递增区间f(x)=2cos^x+根号3*sin2x+a,(1)若x属于R,求f(x)的递增区间(2)当x属于[0,pai/2]时,f(x)
f(x)=2cos^x+根号3sin2x+a,(1)若x属于R,求f(x)的递增区间
f(x)=2cos^x+根号3*sin2x+a,
(1)若x属于R,求f(x)的递增区间
(2)当x属于[0,pai/2]时,f(x)<=4恒成立.求实数a取之范围
f(x)=2cos^x+根号3sin2x+a,(1)若x属于R,求f(x)的递增区间f(x)=2cos^x+根号3*sin2x+a,(1)若x属于R,求f(x)的递增区间(2)当x属于[0,pai/2]时,f(x)
1)导数法可以,也可以利用三角变换的方法.
f(x)=2cos^x+√3*sin2x+a
=cos2x+1+√3sin2x+a
=cos2x+√3sin2x+a+1
=2*(1/2cos2x+√3/2sin2x)+a+1
=2*sin(2x+1/6π)+a+1
设Y=2x+1/6π,因为正弦函数的递增区间为(2Kπ-1/2π,2Kπ+1/2π),
即当Y∈(2Kπ-π/2,2Kπ+π/2)时函数递增,即x∈(Kπ-π/3,Kπ+π/6)为函数的递增区间.
2)当x∈[0,π/2]时,Y=2x+1/6π∈[π/6,7π/6],此时只需研究函数f(Y)=2sinY+a+1,在[π/6,7π/6]区间,当Y=π/2时函数有最大值=2+a+1,另2+a+1≤4,得到a≤1.得出结论.
如果有算错的地方,请见谅!
1)求导数,可以得出
2)f(x)=2cos^x+根号3*sin2x+a=cos2x+根号3*sin2x+a+1
令t=根号3*sin2x,则cos2x=根号(1-t^/9)
求出t的范围,既可求出a的范围