Consider the graph defined by
$$y = \dfrac{x – 3}{x – 5}$$
(a) Use the definition of the derivative to find the slope of the tangent line to the graph at the point $(6, 3)$.
(b) Find an equation of the tangent line to the graph at the point $(6, 3)$.
Best Answer
The definition of the derivative , which gives the slope is $$y_0'=\lim\limits_{x\to x_0}\dfrac{y-y_0}{x-x_0}$$ The equation of the tangent line is $$y-y_0=y'_0(x-x_0)$$ Can you now continue?