Teaching guide
Saddle Point vs Minimum in 3D Graphs
A saddle curves up in one direction and down in another, unlike a true minimum.
Use the interactive graph first, then connect the visual shape to the written rule.
Classroom check
Q: How can students spot a saddle?
A: Rotate and inspect perpendicular slices through the critical point.
Try it yourself
Use the interactive calculator below to experiment with this concept.
Related guides
Graph z=f(x,y)
Type a formula, choose x and y ranges, then rotate the result to inspect slices.
Surface and Contours
Contours are horizontal slices of the 3D graph projected into 2D.
Teacher Setup
Use locked views, hidden formulas, and reveal prompts for classroom embeds.
Export PNG
Use the export button after rotating the graph to the desired angle.