Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 257

\[f^{'}(x) \neq 0.\]

\[1)\ f(x) = ax^{2} - \frac{1}{x^{2}};\]

\[f^{'}(x) = a \bullet 2x - \left( - 2x^{- 3} \right) \neq 0;\]

\[2ax^{4} + 2 \neq 0\]

\[2\left( ax^{4} + 1 \right) \neq 0\]

\[a \geq 0.\]

\[Ответ:\ \ \lbrack 0;\ + \infty).\]

\[2)\ f(x) = ax + \frac{1}{x};\]

\[f^{'}(x) = a + \left( - 1 \bullet x^{- 2} \right) \neq 0;\]

\[ax^{2} - 1 \neq 0\]

\[a \leq 0.\]

\[Ответ:\ \ ( - \infty;\ 0\rbrack.\]

\[3)\ f(x) = ax^{3} + 3x^{2} + 6x;\]

\[f^{'}(x) = a \bullet 3x^{2} + 3 \bullet 2x + 6 \neq 0;\]

\[ax^{2} + 2x + 2 \neq 0\]

\[D = 2^{2} - 4 \bullet a \bullet 2 < 0\]

\[4 - 8a < 0\]

\[8a > 4\]

\[a > 0,5.\]

\[Ответ:\ \ (0,5;\ + \infty).\]

\[4)\ f(x) = x^{3} + 6x^{2} + ax;\]

\[f^{'}(x) = 3x^{2} + 6 \bullet 2x + a \neq 0;\]

\[3x^{2} + 12x + a \neq 0\]

\[D = 12^{2} - 4 \bullet 3 \bullet a < 0\]

\[144 - 12a < 0\]

\[12a > 144\]

\[a > 12.\]

\[Ответ:\ \ (12;\ + \infty).\]

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