Решебник по алгебре и начала математического анализа 11 класс Колягин Задание 1034

\[1)\ y = x^{2} + 6x + 3;\]

\[y^{'}(x) = 2x + 6 \geq 0;\]

\[2x \geq - 6\]

\[x \geq - 3;\]

\[y( - 3) = 9 - 18 + 3 = - 6.\]

\[Ответ:\ \ E(y) = \lbrack - 6;\ + \infty).\]

\[2)\ y = - 2x^{2} + 8x - 1;\]

\[y^{'}(x) = - 2 \bullet 2x + 8 \geq 0;\]

\[4x \leq 8\]

\[x \leq 2;\]

\[y(2) = - 8 + 16 - 1 = 7.\]

\[Ответ:\ \ E(y) = ( - \infty;\ 7\rbrack.\]

\[3)\ y = e^{x} + 1;\]

\[y^{'}(x) = e^{x} + 0 = e^{x} > 0;\]

\[\lim_{x \rightarrow - \infty}\left( e^{x} + 1 \right) = 0 + 1 = 1.\]

\[Ответ:\ \ E(y) = (1;\ + \infty).\]

\[4)\ y = 2 + \frac{2}{x}\]

\[yx = 2x + 2\]

\[x(y - 2) = 2;\]

\[x = \frac{2}{y - 2};\]

\[y - 2 \neq 0\]

\[y \neq 2.\]

\[Ответ:\ \ \]

\[E(y) = ( - \infty;\ 2) \cup (2;\ + \infty).\]