Решебник по алгебре и начала математического анализа 11 класс Алимов Задание 797

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

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

\[3x^{2} = 1\]

\[x^{2} = \frac{1}{3}\]

\[x = \pm \sqrt{\frac{1}{3}} = \pm \sqrt{\frac{3}{9}} = \pm \frac{\sqrt{3}}{3}.\]

\[Ответ:\ \pm \frac{\sqrt{3}}{3}.\]

\[2)\ f(x) = \sqrt[3]{x^{2}} = x^{\frac{2}{3}}\]

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

\[\frac{2}{3\sqrt[3]{x}} = 1\]

\[\frac{1}{\sqrt[3]{x}} = \frac{3}{2}\]

\[\sqrt[3]{x} = \frac{2}{3}\]

\[x = \left( \frac{2}{3} \right)^{3} = \frac{8}{27}.\]

\[Ответ:\ \ \frac{8}{27}.\]