Question

Решить ур-е f ` (x)=0, если f(x)= -1/2x+sin(x-(pi/

Answer 1

$f(x)=-\frac{1}{2}x+sin(x-\frac{\pi}{6})\\\\f'(x)=0\\\\-\frac{1}{2}+cos(x-\frac{\pi}{6})=0\\\\sin(x-\frac{\pi}{6})=\frac{1}{2}\\\\x-\frac{\pi}{6}=(-1)^{n}\cdot \frac{\pi}{6}+\pi n,\; n\in Z\\\\x=\frac{\pi}{6}+(-1)^{n}\cdot \frac{\pi}{6}+\pi n\\\\x=\frac{\pi}{6}\cdot (1+(-1)^{n})+\pi n,\; n\in Z\\\\x= \left \{ {{\pi n,\; esli\; n=2k+1,\; k\in Z(n-nechetnoe)} \atop {\frac{\pi}{3}}+\pi n,\; esli\; n=2k,\; k\in Z(n-chetnoe)}} \right.$