Question

Найдите промежутки монотонности и точки экстремума функции
f(x) =
x
2+6x
x−2

Answer 1

Ответ:

$f(x) = \frac{d}{dx} ( \frac{ {x}^{2} + 6x }{x - 2} ) \\ f(x) = \frac{ \frac{d}{dx} ( {x}^{2} + 6x) \times (x - 2) - ( {x}^{2} + 6x) \times \frac{d}{dx}(x - 2) }{(x - 2) {}^{2} } \\ f(x) = \frac{2x + 6) \times (x - 2) \times ( {x}^{2} + 6x) \times 1 }{ {(x - 2)}^{2} } \\ f(x) = \frac{ {x}^{2} - 4x - 12 }{ {(x - 2)}^{2} }$