Question

Производная)как решать?​

Answer 1

$\displaystyle f(x) = \frac{2x+1}{x-4} = \frac{2x-8+9}{x-4} = 2 + \frac{9}{x-4}\\\\f'(x) = 9\left(\frac{1}{x-4}\right)' = \frac{-9}{(x-4)^2}\\f'(1) = -9/9=-1$

Теперь ищем сами корни

$\displaystyle 2+\frac{9}{x-4} = -1\\\frac{9}{x-4} = -3\\\\x-4 = -3\\x=1$

Единственный корень 1