已知函数f(x)=2cos2x+sin平方x-4cosx

2个回答

  • f(x)=2cos2x+sin^x-4cosx

    =2(2cos^x-1)+(1-cos^x)-4cosx

    =3cos^x-4cosx-1

    f(π/3)=3cos^(π/3)-4cosπ/3-1=3x(1/2)^-4x1/2-1=(-9)/4;

    令t=cosx,t∈[-1,1].F(t)=3(t^2)-4t-1

    F'(t)=6t-4 令F'(t)=0,t=2/3;

    t∈[-1,2/3],F(t)递减,t∈[2/3,1],F(t)递增.

    f(x)(min)=F(2/3)=(-7)/3;

    F(-1)=6,F(1)=-2,f(x)(max)=max{F(-1),F(1)}=6;