lecture17

# lecture17 - 3.9 Related Rates We've already considered the...

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3.9 Related Rates We’ve already considered the derivative as the instantaneous rate of change at a certain point. We can also use derivatives to calculate the rate of change of certain variables based on a known rate of change of other variables. These are called related rates equations . Example Suppose a liquid is draining through a conical ﬁlter. As the liquid drains, its volume V , height h , and radius r change with time t , i.e. V, h, r are functions of t . How does the volume change in relation to the other variables? 1

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Strategy for Solving Related Rates Problems 1. Name 2. Write 3. Identify 4. Determine 5. Diﬀerentiate 6. Evaluate WARNING: Always diﬀerentiate in Step 5 BEFORE substituting in for numerical quantities in Step 6. 2
Example 1 Derek Jeter is stealing third base. He has a speed of 30 ft/sec at the instant he is 20 ft. from third base. At what rate is his distance from home plate changing at that instant? (Note: a baseball diamond is a square whose sides are 90 ft. long). 3

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lecture17 - 3.9 Related Rates We've already considered the...

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