Find the points at which the graph of the equation has a vertical or horizontal tangent line.
A)There is a horizontal tangent at but no vertical tangents.
B)There is a horizontal tangent at and a vertical tangent at .
C)There is a vertical tangent at but no horizontal 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 horizontal tangent at but no vertical tangents. 
B)There is a horizontal tangent at and a vertical tangent at . 
C)There is a vertical tangent at but no horizontal 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 where the graph has a horizontal or vertical tangent line, we need to find where its derivative is undefined or equal to zero.

Differentiating the given equation with respect to x:
y' = 2x-8
Setting y' = 0 to find where the slope is zero:
2x-8 = 0
2x = 8
x = 4
Thus, we have a horizontal tangent at x=4.

Differentiating y' with respect to x to find where the slope of the curve starts decreasing towards negative infinity:
y'' = 2
This is always defined, so there are no points where the slope is undefined. Therefore, there are no vertical tangents.

Hence, we have a horizontal tangent at x=4 and no vertical tangents. The answer is D.

Find the Points at Which the Graph of the Equation