ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 1038

\[y = 6\cos^{2}x + 6\sin x - 2 =\]

\[= 6\left( 1 - \sin^{2}x \right) + 6\sin x - 2 =\]

\[= 6 - 6\sin^{2}x + 6\sin x - 2 =\]

\[= - 6\sin^{2}x + 6\sin x + 4.\]

\[1)\ \sin x_{0} = - \frac{b}{2a} = - \frac{6}{2 \bullet ( - 6)} =\]

\[= \frac{6}{12} = \frac{1}{2};\]

\[y\left( x_{0} \right) = - 6 \bullet \frac{1}{4} + 6 \bullet \frac{1}{2} + 4 =\]

\[= - 1,5 + 3 + 4 = 5,5;\]

\[f(0) = - 6 \bullet 0^{2} + 6 \bullet 0 + 4 = 4;\]

\[f(1) = - 6 \bullet 1^{2} + 6 \bullet 1 + 4 =\]

\[= - 6 + 6 + 4 = 4.\]

\[2)\ Точки\ максимума:\]

\[\sin x = \frac{1}{2}\]

\[x = ( - 1)^{n} \bullet \arcsin\frac{1}{2} + \pi n =\]

\[= ( - 1)^{n} \bullet \frac{\pi}{6} + \pi n.\]

\[Ответ:\ \ ( - 1)^{n} \bullet \frac{\pi}{6} + \pi n.\]