Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 1502

\[\boxed{\mathbf{1502}\mathbf{.}}\]

\[f(x) = \frac{x^{3} + 1}{3}\]

\[\mathbf{С}\mathbf{\ }осью\ Ox\ (y = 0):\]

\[\frac{x^{3} + 1}{3} = 0\]

\[x^{3} + 1 = 0\]

\[x^{3} = - 1\]

\[x = - 1.\]

\[f^{'}(x) = \frac{1}{3} \bullet \left( \left( x^{3} \right)^{'} + (1)^{'} \right) =\]

\[= \frac{1}{3} \bullet \left( 3x^{2} + 0 \right) = \frac{3x^{2}}{3} = x^{2};\]

\[f^{'}( - 1) = ( - 1)^{2} = 1;\]

\[f( - 1) = \frac{( - 1)^{3} + 1}{3} =\]

\[= \frac{- 1 + 1}{3} = \frac{0}{3} = 0;\]

\[y = 0 + 1(x + 1) = x + 1.\]

\[Ответ:\ \ y = x + 1.\]