Question

Алгебра, производная, 80 баллов

Answer 1

$y'=\frac{4}{3}cos\frac{x}{3}+\frac{4\sqrt3}{3}sin\frac{x}{3}=\frac{4}{3}(cos\frac{x}{3}+\sqrt3sin\frac{x}{3})<0\\\\cos\frac{x}{3}+\sqrt3sin\frac{x}{3}<0|:cos\frac{x}{3}\ne 0\\\\1+\sqrt3tg\frac{x}{3}<0\\\\tg\frac{x}{3}<-\frac{1}{\sqrt3}\\\\-\frac{\pi}{2}+\pi n<\frac{x}{3}<-\frac{\pi}{6}+\pi n\\\\-\frac{3\pi }{2}+3\pi n<x<-\frac{\pi}{2}+3\pi n,n\in Z$

$-\frac{3\pi}{2}+3\pi n<x<-\frac{\pi}{2}+3\pi n,n\in Z$