Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 258

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

\[1)\ f(x) = ax^{7} + x^{3} - 1;\]

\[f^{'}(x) = a \bullet 7x^{6} + 3x^{2} \geq 0;\]

\[x^{2} \bullet \left( 7ax^{4} + 3 \right) \geq 0\]

\[a \geq 0.\]

\[Ответ:\ \ \lbrack 0;\ + \infty).\]

\[2)\ f(x) = x^{5} + ax^{3} + 3;\]

\[f^{'}(x) = 5x^{4} + a \bullet 3x^{2} \geq 0;\]

\[x^{2} \bullet \left( 5x^{2} + 3a \right) \geq 0\]

\[a \geq 0.\]

\[Ответ:\ \ \lbrack 0;\ + \infty).\]

\[3)\ f(x) = (x + a)\sqrt{x};\]

\[f^{'}(x) = \sqrt{x} + (x + a) \bullet \frac{1}{2\sqrt{x}} \geq 0;\]

\[2x + x + a \geq 0\]

\[3x + a \geq 0\]

\[a \geq 0.\]

\[Ответ:\ \ \lbrack 0;\ + \infty).\]

\[4)\ f(x) = x + \frac{a}{x};\]

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

\[x^{2} - a \geq 0\]

\[a \leq 0.\]

\[Ответ:\ \ ( - \infty;\ 0\rbrack.\]