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An interactive three dimensional plot with axes labeled
\(x\text{,}\) and
\(y\text{,}\) and
\(z\text{.}\) A black curve is plotted that is centered and the origin, moves around the z-axis, and has two maximums and two minimums as the curve completes one rotation around the z-axis. The slider at the top of the figure changes the location of a highlighted point on the black curve. at the highlighted point on the black curve, a red line is drawn that is tangent to the curve at the highlighted point. The second slider controls how small of a neighborhood is plotted around the highlighted point.