作业帮f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 04:26:50
![f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值](/uploads/image/z/6121237-13-7.jpg?t=f%28x%29%3D2sin%26%23178%3B%28%CF%80%2F4%2Bx%29-%E2%88%9A3cos2x%2Cx%E2%88%88%5B%CF%80%2F4%2C%CF%80%2F2%5D%2C%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%9C%80%E5%B0%8F%E5%80%BC)
f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值
f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值
f(x)=2sin²(π/4+x)-√3cos2x,x∈[π/4,π/2],求f(x)的最大值最小值
f(x)=1-cos2(π/4+x)-√3cos2x
=1-cos(π/2+2x)-√3cos2x
=sin2x-√3cos2x+1
=2(1/2sin2x-√3/2cos2x)+1
=2sin(2x-π/3)+1
sin(2x-π/3)=1的时候,f(X)最大值=2+1=3
sin(2x-π/3)=-1的时候,f(X)最小值=-2+1=-1