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Home Partial Differentiation Surfaces Examples Example 8: 'Beaker Spout' Shaped Curve
 
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Example 8: 'Beaker Spout' Shaped Curve

Graph the function 11_partial_differentiation-48.gifwhere

11_partial_differentiation-49.gif11_partial_differentiation-50.gif11_partial_differentiation-51.gif

Step 1

The topographic map has level curves

11_partial_differentiation-52.gif

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

The table shows that the curves are bell shaped.

11_partial_differentiation-54.gif
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

11_partial_differentiation-55.gif

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.

11_partial_differentiation-56.gif

Figure 11.1.20

 
Home Partial Differentiation Surfaces Examples Example 8: 'Beaker Spout' Shaped Curve

Last Update: 2006-11-15