Question

求函数f(x)=3sinx+cos2x的最大值和最小值

Answer 1

f(x)=3sinx+cos2x=3sinx+1-2(sinx)^2
=-2sinxsinx+3sinx+1
=-2(sinx-3/4)^2+1+9/8
当sinx=3/4，f(x)最大值17/8
又-1<=sinx<=1,当sinx=-1时f(x)最小值-4

Answer 2

f(x)=3sinx+cos2x
=3sinx+1-2sin^2x
=-2(sin^2x -3sinx/2 +9/16)+1+9/8
=-2(sinx-3/4)^2+17/8
当sinx=3/4时有最大值 f(x)=17/8
当sinx=-1时有最小值f(x)=-32/16