Предмет: Алгебра, автор: Michael12341

Решите пожалуйста, фото прикрепил

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Автор ответа: NNNLLL54

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Уравнение касательной : $\bf y=f(x_0)+f'(x_0)(x-x_0)$ .

$\bf f(x)=\dfrac{4}{x}+\dfrac{x}{4}\ \ ,\ \ x_0=5\\\\f(5)=\dfrac{4}{5}+\dfrac{5}{4}=\dfrac{41}{20}=2,05\\\\f'(x)=-\dfrac{4}{x^2}+\dfrac{1}{4}\ \ ,\ \ \ f'(5)=-\dfrac{4}{25}+\dfrac{1}{4}=\dfrac{9}{100}=0,09\\\\y=2,05+0,09(x-5)\\\\\boxed{\bf \ y=0,09\, x+1,6\ }$

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