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Example 8: 'Beaker Spout' Shaped Curve

Graph the function 11_partial_differentiation-48.gifwhere


Step 1

The topographic map has level curves


The derivative dx/dy = 4y(c - y2) has zeros at y = 0 and y = ± √c.

The table shows that the curves are bell shaped.


Step 2 Draw the rectangular solid.
Step 3

The surface intersects the plane x = 0 in the parabola z = y2, and intersects the plane y = 0 in the curve


It intersects the plane z = 1 in the curve

x = (1 - y2)2.

Step 4

The surface, shown in Figure 11.1.20, is shaped like a beaker spout.


Figure 11.1.20


Last Update: 2006-11-15