Use graphical methods to find any turning points of the graph of the function.
-$$y = \frac { 6 x } { x ^ { 2 } + 1 }$$
A) $( 1,0 )$ and $( - 1,0 )$
B) $( 0,0 )$
C) $( - 1 , - 3 )$ and $( 1,3 )$
D) $( 0,0 )$ and $( 1,0 )$

Question

Quizplus · Accepted Answer

To find the turning points of the function $y = \frac { 6 x } { x ^ { 2 } + 1 }$, we differentiate it with respect to $x$ to find the critical points. The derivative is $y' = \frac{6(1-x^2)}{(x^2+1)^2}$. Setting $y'$ to 0 gives $x^2 = 1$, so $x = \pm 1$. Substituting these values back into the original function gives the turning points $( - 1 , - 3 )$ and $( 1,3 )$.

Use Graphical Methods to Find Any Turning Points of the Graph