Question

已知函数f（c）=2cos2x+sin^2x 〈1〉求f〈兀/3〉的值； （2）求f（x）的最大

Answer 1

f（x）=2cos2x+sin^2x

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

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

=-3sin^2x+2

(1)f(π/3)=-3sin^2(π/3)+2

=-3×(3/4)+2

=-1/4

(2)当sin^2x=0时,f(x)有最大值2

当sin^2x=1时,f(x)有最小值-1