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An interactive three dimensional plot with axes labeled
\(x\text{,}\) \(y\text{,}\) and
\(z\) and a coordinate grid shown on the xy-plane. A dropdown box allows the user to select “Local Minimum”, “Local Maximum”, or “Saddle Point”. For the “Local Minimum” option, an upward facing circular paraboloid is shown above the xy-plane. For the “Local Maximum” option, a downward facing circular paraboloid is shown above the xy-plane. For the “Saddle Point” option, a saddle surface centered at the origin is shown. There is a slider above the figure that allows the user to change the direction of a red curve along the selected surface. For the “Local Maximum” option, the red curve is concave down for any direction. For the “Local Minimum” option, the red curve is concave up for any direction. For the “Saddle Point” option, the red curve is concave down for some directions and concave up for others.