给跪了，求本题解

f=sin(2x)cos(x)=2sin(x)cos^2(x)=2sin(x)[1-sin^2(x)]
=2sin(x)[1+sin(x)][1-sin(x)]
令z=sin(x)
则:f=2z(1-z^2)=2(z-z^3)
导数求极值，f'=2(1-3z^2)=0
得：z^2=1/3,z=+-[根号(3)]/3
即：sin(x)=+-[根号(3)]/3 时，f有极值。
极值为：(4/9)[根号(3)]