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GeoGebraGeoGebra Classroom

Visualization of Saddle Point and Partial Deriv's

A visualization of a surface with a saddle point. You can change the value of k with the slider and simultaneously see the level curve corresponding to k (in teh 2D window), as well as the intersection of the horizontal plane at height k with the surface. What characteristics do the level curves have when k>0? when k=0? when k<0? How does your answer relate to what we have learned about extrema of functions and saddle points? You can also rotate the 3D graph to get a better view by right clicking and dragging the 3D graph.