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Home Partial Differentiation Surfaces Examples Example 4: Hyperbolic Paraboloid
 
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Example 4: Hyperbolic Paraboloid

Graph the function

11_partial_differentiation-33.gif

where - 3 ≤ x ≤ 3, - 2 ≤ y ≤ 2, - 1 ≤ z ≤ 1. This is a hyperbolic paraboloid (Figure 11.1.16).

11_partial_differentiation-35.gif

Draw a topographic map. The level curves are hyperbolas.

11_partial_differentiation-36.gif

Draw the axes and rectangular solid.

11_partial_differentiation-37.gif

Draw the curves where the surface intersects the faces and also the planes x = 0, y = 0. The topographic map gives the curves on z = -1, z = 0, and z = 1. The curves on x = 0 and y = 0 are parabolas.

11_partial_differentiation-38.gif

Figure 11.1.16

Complete Figure 11.1.16.

 
Home Partial Differentiation Surfaces Examples Example 4: Hyperbolic Paraboloid

Last Update: 2006-11-15