已知函数f(x)=sin2xcos2x-根号3sin²2x,求f(x)在区间[0,π/4]上的取值范围
问题描述:
已知函数f(x)=sin2xcos2x-根号3sin²2x,求f(x)在区间[0,π/4]上的取值范围
答
f*x(=1/2*sin4x-√3(1-cos4x)/2
=sin4xcosπ/3+cos4xsinπ/3-√3/2
=sin(4x+π/3)-√3/2
π/3所以-√3/2在减去-√3/2
值域[-√3,1-√3/2]