Find the points at which the graph has vertical and horizontal tangents

Thread starter calculusisfun
Start date Sep 7, 2010
Tags

Graph Horizontal Points Vertical

In summary, a graph has a vertical tangent when the slope of the curve is undefined, meaning that the tangent line is perpendicular to the x-axis. To find these points, you can set the derivative equal to zero and solve for the x-values. A horizontal tangent, on the other hand, has a slope of zero and the tangent line is parallel to the x-axis. The first derivative test can be used to find these points by evaluating the derivative at critical points. Points of vertical and horizontal tangency are important because they provide information about the behavior of the graph and can be useful in applications such as optimization problems.

Sep 7, 2010

calculusisfun

PRObLEM SOLVED> :)

Last edited: Sep 7, 2010

Physics news on Phys.org

Sep 7, 2010

Samuelb88

You're values for x, and y for which the graph of the equation obtains a horizontal or vertical asymptote seem to be correct. But be careful, the question asks for points, not values!

Sep 7, 2010

calculusisfun

Problem solved :)

Last edited: Sep 7, 2010

Sep 7, 2010

Mentallic

Homework Helper

What about [itex]x=\pm 3[/itex]?

Sep 7, 2010

calculusisfun

Thanks Metanllic, I just figured it out now. Thanks guys! :)

1. What does it mean for a graph to have a vertical tangent?

A vertical tangent is a point on a graph where the slope of the curve is undefined. This means that at that point, the tangent line is perpendicular to the x-axis and has an undefined slope.

2. How can I find the points at which a graph has vertical tangents?

To find the points at which a graph has vertical tangents, you can use the derivative of the function. Set the derivative equal to zero and solve for the x-values. These x-values will correspond to the points where the graph has vertical tangents.

3. What does it mean for a graph to have a horizontal tangent?

A horizontal tangent is a point on a graph where the slope of the curve is equal to zero. This means that at that point, the tangent line is parallel to the x-axis and has a slope of zero.

4. How can I find the points at which a graph has horizontal tangents?

To find the points at which a graph has horizontal tangents, you can use the first derivative test. Find the critical points of the function and then evaluate the derivative at those points. If the derivative is equal to zero, then the point is a potential point of horizontal tangency.

5. Why are points of vertical and horizontal tangency important?

Points of vertical and horizontal tangency are important because they can provide valuable information about the behavior of the graph. They can help determine the maximum and minimum values of the function, as well as the concavity of the graph. They are also useful in applications such as optimization problems.