Question

Решите неравенство f'(x)>0, если f(x)=cos4x+2x.

Answer 1

$f(x)=cos4x+2x\\f'(x)=-4sin4x+2\ \textgreater \ 0\\sin4x\ \textless \ \frac{1}{2}\\4x\in(\frac{\pi}{6}+2\pi n; \frac{5\pi}{6}+2\pi n)\\x\in(\frac{\pi}{24}+\frac{\pi n}{2};\frac{5\pi }{24} +\frac{\pi n}{2})$