f(x)=d/dx(2sin(x/2)2
f(x)=2×d/dx(g2)×d/dx(sinx/2)
f(x)=2×2g×cos(x/2)×1/2
f(x)=2×2sin(x/2)cos(x/2)×1/2
f(x)=sinx
f(x)= 3cosx+cos3x =3cosx+4cos³x -3sinx = 4cos³x
мах f(x) = f(0)= 4cos³0 =4*1 = 4 ;
min f(x) = f(π)= 4cos³π =4*(-1) = - 4 .
! * * * cos3x =cos(2x+x) =cos2x*cosx - sin2x*sinx =(cos²x -sin²x) *cosx - 2sinx*cosx*sinx =cosx *(cos²x - sin²x - 2sin²x) =cosx *(cos²x - 3sin²x) =
cosx *(cos²x - 3(1 - cos²x) ) = cosx(4cos²x - 3) || 4cos³x - 3cosx || * * *
Объяснение:
f(x)=d/dx(2sin(x/2)2
f(x)=2×d/dx(g2)×d/dx(sinx/2)
f(x)=2×2g×cos(x/2)×1/2
f(x)=2×2sin(x/2)cos(x/2)×1/2
f(x)=sinx
f(x)= 3cosx+cos3x =3cosx+4cos³x -3sinx = 4cos³x
мах f(x) = f(0)= 4cos³0 =4*1 = 4 ;
min f(x) = f(π)= 4cos³π =4*(-1) = - 4 .
! * * * cos3x =cos(2x+x) =cos2x*cosx - sin2x*sinx =(cos²x -sin²x) *cosx - 2sinx*cosx*sinx =cosx *(cos²x - sin²x - 2sin²x) =cosx *(cos²x - 3sin²x) =
cosx *(cos²x - 3(1 - cos²x) ) = cosx(4cos²x - 3) || 4cos³x - 3cosx || * * *
Объяснение: