Assume that the number of homicide in Chicago can be modeled by the function

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?