Предмет: Алгебра, автор: irinaslasten97

Напишите уравнение касательной к графику ф-ии в точке:
$f(x)= e^{1-x} ; x_{0}=1$

Ответы

Автор ответа: Аноним

Запишем уравнения касательной в общем виде:
y(x) = y₀ + y'(x₀)(x - x₀)

Теперь найдем производную:
$y' = (e^{x-1})' = e^{-1+x}$
следовательно:
f'(1) = e^{-1+ 1} = 1
В результате имеем:
y(x) = y₀ + y'(x₀)(x - x₀)
y(x) = 1 + 1(x - 1)= 1

Ответ: y(x) = 1

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