Решебник по алгебре 11 класс Никольский Параграф 4. Производная Задание 11

\[\boxed{\mathbf{11}\mathbf{.}}\]

\[f(x) = x^{2} - 6x + 11\]

\[\textbf{а)}\ f^{'}(x) = \left( x^{2} - 6x + 11 \right)^{'} =\]

\[= \left( x^{2} \right)^{'} - 6(x)^{'} + (11)^{'} =\]

\[= 2x^{2 - 1} - 6 \cdot 1 + 0 = 2x - 6.\]

\[\textbf{б)}\ tg\ a = f^{'}( - 1) = 2 \cdot ( - 1) -\]

\[- 6 = - 2 - 6 = - 8;\]

\[tg\ a = f^{'}(0) = 2 \cdot 0 - 6 = - 6;\]

\[tg\ a = f^{'}(2) = 2 \cdot 2 - 6 =\]

\[= 4 - 6 = - 2.\]

\[\textbf{в)}\ f^{'}(x) = 0:\]

\[2x - 6 = 0\]

\[2x = 6\]

\[x = 3.\]

\[f^{'}(x) = 1:\]

\[2x - 6 = 1\]

\[2x = 7\]

\[x = 3,5.\]

\[f^{'}(x) = 3:\]

\[2x - 6 = 3\]

\[2x = 9\]

\[x = 4,5.\]