Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 173

\[1)\ f(x) = x^{2} - 7x + 10;\]

\[f^{'}(x) = 2x - 7 < 0\]

\[2x < 7\]

\[x < 3,5.\]

\[Ответ:\ \ ( - \infty;\ 3,5).\]

\[2)\ f(x) = - x^{2} + 4x;\]

\[f^{'}(x) = - 2x + 4 < 0\]

\[2x > 4\]

\[x > 2.\]

\[Ответ:\ \ (2;\ + \infty).\]

\[3)\ f(x) = - 3x^{3} + 3x^{2} + 4;\]

\[f^{'}(x) = - 3 \bullet 3x^{2} + 3 \bullet 2x < 0\]

\[9x^{2} - 6x > 0\]

\[3x(3x - 2) > 0\]

\[x < 0;\ \ \ x > \frac{2}{3}.\]

\[Ответ:\ \ ( - \infty;\ 0) \cup \left( \frac{2}{3};\ + \infty \right).\]

\[4)\ f(x) = (1 - 3x)^{3};\]

\[f^{'}(x) = - 3 \bullet 3(1 - 3x)^{2} < 0\]

\[(1 - 3x)^{2} > 0\]

\[3x \neq 1\]

\[x \neq \frac{1}{3}.\]

\[Ответ:\ \ \left( - \infty;\ \frac{1}{3} \right) \cup \left( \frac{1}{3};\ + \infty \right).\]