Решебник по алгебре 11 класс Никольский Параграф 5. Применение производной Задание 34

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\[\textbf{а)}\ f(x) = x^{e};\ \ x_{0} = e\]

\[f^{'}(x) = ex^{e - 1};\]

\[k = f'(e) = ee^{e - 1} = e^{e};\]

\[y_{0} = f(e) = e^{e};\]

\[y - y_{0} = k\left( x - x_{0} \right)\]

\[y - e^{e} = e^{e}(x - e)\]

\[y - e^{e} = e^{e}x - e^{e + 1}\]

\[y = e^{e}x - e^{e + 1} + e^{e}.\]

\[\textbf{б)}\ f(x) = e^{x};\ \ x_{0} = e\ \]

\[f^{'}(x) = e^{x};\]

\[k = f^{'}(e) = e^{e};\]

\[y_{0} = f(e) = e^{e};\]

\[y - y_{0} = k\left( x - x_{0} \right)\]

\[y - e^{e} = e^{e}(x - e)\]

\[y - e^{e} = e^{e}x - e^{e + 1}\]

\[y = e^{e}x - e^{e + 1} + e^{e}.\]