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:

1. Make sure you have the latest version of Java 7 installed in your computer. Tablets and smartphones are not supported.