Question

已知函数f(x)=2cos2x+sinx^2 (1)求f(π/3)的值； (2)求f(x)的最大值和最小值.

Answer 1

f(x)=2cos2x+sinx^2

=2(1-2sinx^2)+sinx^2

=-3sinx^2+2

f(π/3)=-3[sin(π/3)]^2+2

=-3x3/4+2

=-1/4

(2)求f(x)的最大值和最小值.

易知当sinx=0时有最大值为,2

当sinx=1或-1时有最小值为,-1