## Tangent plane

*Scroll down to the bottom to view the interactive graph.*

A tangent plane to a function \(f(x,y)\) at a point \(P (x_0,y_0)\) is the plane which contains all tangent lines along all traces through \(P\). The following diagram illustrates this idea.

We say that \(f(x,y)\) is differentiable at \(P(x_0,y_0)\) if such a plane exists at \(P\). In this case we can find the plane by using only the trajectories parallel to the \(xz\)-plane and the \(yz\)-plane.

**To view the interactive graph:**

- Make sure you have the latest version of Java 7 installed in your computer. Tablets and smartphones are not supported.
- Download this file, tangentplane.ggb.
- Click here to open GeoGebra.
- After you open GeoGebra, click "File" in the toolbar, then click "Open".
- Choose the .ggb file you just downloaded and click the "Open" button.
- Now you should be able to view the graph inside GeoGebra.

To rotate the graph, **right click and drag**.

Joseph Lo