ГДЗ по алгебре и начала математического анализа 11 класс Колягин Задание 263

\[y = \frac{4}{x};\text{\ \ \ }(1;\ 4).\]

\[1)\ y^{'}(x) = 4 \bullet \left( - \frac{1}{x^{2}} \right);\]

\[y^{'}(1) = - \frac{4}{1^{2}} = - 4;\]

\[y = 4 - 4(x - 1) = 8 - 4x.\]

\[2)\ 8 - 4x = 0\]

\[4x = 8\]

\[x = 2;\]

\[y = 8 - 4 \bullet 0 = 8 - 0 = 8.\]

\[S = \frac{1}{2}xy = \frac{1}{2} \bullet 2 \bullet 8 = 8.\]

\[Ответ:\ \ 8.\]