## Absolute extrema of a function with two constraints

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

This graph shows the constaint set \[g(x,y,z) = x^2+z^2-2 = 0 \quad \text{and} \quad h(x,y,z) = y - z = 0\] as a blue curve. The objective is to find the maximum and minimum of \[f(x,y,z) = -2x+3y-5z\] on the constraint set by looking at the level surface of \(f(x,y,z)\).

**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, lagrange2constraints.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