Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1617

\[\boxed{\mathbf{1617}\mathbf{.}}\]

\[f(x) = 2x^{2} - 3x + 8;\]

\[f^{'}(x) = 2\left( x^{2} \right)^{'} - (3x - 8)^{'} =\]

\[= 2 \bullet 2x - 3 = 4x - 3;\]

\[f^{'}(a) = 4a - 3\ \ и\ \ f(a) =\]

\[= 2a^{2} - 3a + 8;\]

\[y =\]

\[= 2a^{2} - 3a + 8 + (4a - 3)(x - a) =\]

\[= 2a^{2} - 3a + 8 + 4ax - 4a^{2} - 3x + 3a =\]

\[= - 2a^{2} + 4ax - 3x + 8.\]

\[O(0;\ 0):\]

\[0 = - 2a^{2} + 4a \bullet 0 - 3 \bullet 0 + 8\]

\[2a^{2} = 8\]

\[a^{2} = 4\]

\[a = \pm 2.\]

\[y_{1} = 2 \bullet ( - 2)^{2} - 3 \bullet ( - 2) + 8 =\]

\[= 8 + 6 + 8 = 22;\]

\[y_{2} = 2 \bullet 2^{2} - 3 \bullet 2 + 8 =\]

\[= 8 - 6 + 8 = 10.\]

\[Ответ:\ \ ( - 2;\ 22);\ \ (2;\ 10).\]