Checking the previous example with Functions of Two Variables

Use the Show menu to put the applet in input mode.
Enter the input .1*(x^6 + y^3 + 6*x -12*y + 7).

To visualize this function we need to get our scales right.
The factor of .1 in the function is to scale the output.
For the input set:   xMin=-2,   xMax=2,   yMin=-2.5,   yMax=2.5

Click the 'plot' button.
Now use the Show menu to put the applet in level curves mode.
Check the 'show all contour lines' box.

Use the slider on the bottom left to explore the level curves and verify that (-1,-2) is a saddle and (-1,2) is minimum.