Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 234

\[y = x^{3} - x - 1;\text{\ \ \ }\]

\[g(x) = 3x^{2} - 4x + 1.\]

\[1)\ y^{'}(x) = 3x^{2} - 1;\ \]

\[y^{'}(x) = 3 \bullet 2x - 4;\]

\[3x^{2} - 1 = 6x - 4\]

\[3x^{2} - 6x + 3 = 0\]

\[x^{2} - 2x + 1 = 0\]

\[(x - 1)^{2} = 0\]

\[x - 1 = 0\]

\[x = 1.\]

\[2)\ y(1) = 1 - 1 - 1 = - 1;\]

\[y^{'}(1) = 3 - 1 = 2;\]

\[y = - 1 + 2(x - 1) = 2x - 3.\]

\[3)\ y(1) = 3 - 4 + 1 = 0;\]

\[y^{'}(1) = 6 - 4 = 2;\]

\[y = 0 + 2(x - 1) = 2x - 2.\]

\[Ответ:\ \ (1;\ - 1);\ y = 2x - 3;\ \ \]

\[\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }(1;\ 0);\ y = 2x - 2.\]