## Exploring level curves with Functions of Two Variables

Use the **Show** menu to put the applet in input mode.

Choose the input *x^2 - y^2 + 3* from the drop-down list
and click the 'plot' button.

Use the **Show** menu to put the applet in level curves mode.

Check the 'show all contour lines' box.

Move the slider on the bottom left
back and forth and watch the yellow contour move.

Explain what is happening as the slider goes through *z* = 3.

Now use the
**Show** menu to put the applet back in in input mode and
choose input *x^2+y^2 + 1*.

Before going back to level curves
mode predict what the level curves will look like.

What will they look like around the minimum at *(x,y) = (0,0)*?