Find the points at which the graph of the equation has a vertical or horizontal tangent line.
A) There is a vertical tangent at but no horizontal tangents.
B) There is a horizontal tangent at and a vertical tangent at .
C) There is a horizontal tangent at but no vertical tangents.
D) There is a horizontal tangent at and a vertical tangent at .
E) There are no horizontal or vertical tangent lines.

Question

Find the points at which the graph of the equation has a vertical or horizontal tangent line. 
A) There is a vertical tangent at but no horizontal tangents. 
B) There is a horizontal tangent at and a vertical tangent at . 
C) There is a horizontal tangent at but no vertical tangents. 
D) There is a horizontal tangent at and a vertical tangent at . 
E) There are no horizontal or vertical tangent lines.

Quizplus · Accepted Answer

To find vertical tangent lines, we need to find where the derivative of the equation is undefined or infinite. This occurs at x = 2. To find horizontal tangent lines, we need to find where the derivative is equal to zero. Taking the derivative of the equation, we get y' = -4x/(2x^2+1)^2. Setting y' equal to zero, we get -4x = 0, which gives x = 0. Plugging x = 0 back into the original equation, we get y = -5, so the point (0,-5) is the point of horizontal tangency.

Find the Points at Which the Graph of the Equation