Question

已知函数f(x)=2cos2x+sin^2 x.求f(x)的最大和最小值

Answer 1

f(x)=2cos2x+sin^2 x

=2(2cos^2x-1)+sin^2 x

=4cos^2x-2+sin^2 x

=3cos^2x-2+1

=3cos^2x-1

∵0≤cos^2x≤1

∴-1≤3cos^2x-1≤2