1.
f (x) = 12x - x³
f'(x) = 12 - 3x²
12 - 3x² ≤ 0
3·(4 - x²) ≤ 0
3·(2 - x)·(2 + x) ≤ 0
(-) (+) (-)
--- (-2) --- (2) ---> x
x ∈ (-∞; -2] ∪ [2; +∞)
2.
f (x) = cos 2x + x·√3, x ∈ [0; 4π]
f'(x) = -2sin 2x + √3
-2sin 2x + √3 = 0
![sin 2x=\frac{ \sqrt{3} }{2} \\ \\ \left \{ {{2x=(-1)^n* \frac{ \pi }{3}+ \pi n,nEZ } \atop {xE[0;4 \pi ]}} \right. \\ \\ \left \{ {{x=(-1)^n* \frac{ \pi }{6}+ \frac{ \pi n}{2} ,nEZ } \atop {xE[0;4 \pi ]}} \right.](https://tex.z-dn.net/?f=+sin+2x%3D%5Cfrac%7B+%5Csqrt%7B3%7D+%7D%7B2%7D++%5C%5C++%5C%5C++%5Cleft+%5C%7B+%7B%7B2x%3D%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B3%7D%2B+%5Cpi+n%2CnEZ+%7D+%5Catop+%7BxE%5B0%3B4+%5Cpi+%5D%7D%7D+%5Cright.++%5C%5C++%5C%5C+%5Cleft+%5C%7B+%7B%7Bx%3D%28-1%29%5En%2A+%5Cfrac%7B+%5Cpi+%7D%7B6%7D%2B++%5Cfrac%7B+%5Cpi+n%7D%7B2%7D+%2CnEZ+%7D+%5Catop+%7BxE%5B0%3B4+%5Cpi+%5D%7D%7D+%5Cright. "sin 2x=\frac{ \sqrt{3} }{2} \\ \\ \left \{ {{2x=(-1)^n* \frac{ \pi }{3}+ \pi n,nEZ } \atop {xE[0;4 \pi ]}} \right. \\ \\ \left \{ {{x=(-1)^n* \frac{ \pi }{6}+ \frac{ \pi n}{2} ,nEZ } \atop {xE[0;4 \pi ]}} \right.")
x ∈ {π/6, π/3, 7π/6, 4π/3, 13π/6, 7π/3, 19π/6, 10π/3}