### Find the derivative using implicit differentiation

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1. Assume that the number of homicide in Chicago can be modeled by the function R(t) below, where t is the time since year 2000. What does R'(4) represent?

2. Assume that the rate of homicide in Chicago can be modeled by the function R(t) below, where t is the time since year 2000. Compute the values of R'(4) and R'(6) and explain the difference.

3. If you drop a rock off a bridge and its distance is given by H(t) in ft where t is in seconds, then what is the velocity of the rock after 2 seconds?

4. Find the derivative using implicit differentiation.

5. Assume that C(x) represents the cost of producing x calculators. If C(100) = \$500 and C'(100) = \$4.75, what is the average cost of a calculator when producing 100 calculators?

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