1) y' = 12 - 1/х
12 - 1/х = 0
1/х = 12
х = 1/12∈[1/24; 5/24]
-∞ 1/24 1/12 5/24 +∞
- + знаки производной 12 - 1/х
уmin = 12*1/12 - ln(12*1/12) +4 = 12 - 0 +4 = 16
2) 2Sin(x +π/3) + Cos2x = Sinx -1
2(Sinx*Cosπ/3 +Cosx*Sinπ/3) + Cos²x - Sin²x = Sinx -1
2(Sinx*1/2 + Cosx*√3/2) + Cos²x - Sin²x -Sinx +1 = 0
Sinx +√3Cosx + Cos²x - Sin²x -Sinx +1 = 0
√3Cosx + Cos²x - Sin²x +1 = 0
√3Cosx + Cos²x + Cos²x = 0
√3Cosx + 2Cos²x = 0
Cosx(√3 +2Cosx) = 0
Cosx = 0 или √3 + 2Cosx = 0
x = π/2 + πk , k ∈Z Cosx = -√3/2
x = +-5π/6 + 2πn , n∈Z