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Example 6

A rectangular solid has sides x, y, and z. Find the rate of change of the volume V = xyz if x = 1, y = 2, z = 3 (in feet),

11_partial_differentiation-314.gif (in feet per second).

We have

11_partial_differentiation-315.gif

so

11_partial_differentiation-316.gif

Thus the volume is decreasing at -5 cubic feet per second (Figure 11.5.6).

11_partial_differentiation-317.gif

Figure 11.5.6


Last Update: 2006-11-15