Provide an appropriate response.
-Find all points $( x , y )$ on the graph of $y = \frac { x } { ( x - 5 ) }$ with tangent lines perpendicular to the line $y = 5 x - 4$.
A) $( 10,2 )$
B) $( 0,0 ) , ( 5,2 )$
C) $( 0,0 )$
D) $( 0,0 ) , ( 10,2 )$

Question

Quizplus · Accepted Answer

To have a tangent line that is perpendicular to $y = 5x-4$, the slope of the tangent line must be $\frac{-1}{5}$. We can find the slope of the tangent line by implicitly differentiating $y = \frac { x } { ( x - 5 ) }$ to get $\frac{dy}{dx} = \frac{5}{(x-5)^2}$. For the slope to be $\frac{-1}{5}$, we need $x = 0$ or $x = 10$. When $x = 0$, $y = 0$, and when $x = 10$, $y = 2$. Therefore, the points are $(0,0)$ and $(10,2)$ which are both in choice D.

Provide an Appropriate Response (x,y)( x , y )(x,y) On the Graph Of

Provide an Appropriate Response $( x , y )$ On the Graph Of