Решебник по алгебре 11 класс Никольский Параграф 5. Применение производной Задание 12

\[\boxed{\mathbf{12}\mathbf{.}}\]

\[\textbf{а)}\ y = \cos x + \frac{\sqrt{3}}{2}x\]

\[y^{'} = - \sin x + \frac{\sqrt{3}}{2};\]

\[- \sin x + \frac{\sqrt{3}}{2} = 0\]

\[\sin x = \frac{\sqrt{3}}{2}\]

\[x_{1} = \frac{\pi}{3} + 2\pi n;\]

\[x_{2} = \frac{2\pi}{3} + 2\pi n.\]

\[\textbf{б)}\ y = 2\sin x + \sqrt{2}x\]

\[y^{'} = 2\cos x + \sqrt{2};\]

\[2\cos x + \sqrt{2} = 0\]

\[2\cos x = - \sqrt{2}\]

\[\cos x = - \frac{\sqrt{2}}{2}\]

\[x_{1} = \frac{3\pi}{4} + 2\pi n;\]

\[x_{2} = \frac{5\pi}{4} + 2\pi n.\ \]