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Extra Credit (earn up to 3 points) Can you have a point on the graph of a function that is both an inflection point and a critical point?  Explain your answer and provide a sketch to receive any credit.  

Solve  for t.  Round answer to two decimal places. 

**Partial Credit Problem**  (8 points total) Note: To receive any credit, show all supporting work and use the Calculus techniques developed not the shortcuts with your calculator unless otherwise indicated.  You may use either the first or second derivative test and show all work to receive credit.  The annual profit function for a manufacturer of precision gauges is modeled by the function

For the graph given below match the point indicated with the most appropriate description. 

**Partial Credit Problem**  (3 points total) Indicate if the following statement is true or false. To earn full credit,  If the statement is false, explain why or give an example that disproves the statement in your submitted handwritten work.   True or False: For a function the average rate of change is the same as the instantaneous rate of change.

Suppose we have the function

For each function choose the most appropriate strategy/rule for determining the derivative  1) For  you would use [1]. 2) For

The table below lists possible steps in an approach to a calculus problem.   A) Determine critical values. B) Determine the second derivative. C) Set the second derivative equal to zero. D) Choose test points for intervals determined by critical numbers and test in the original function E) Choose test points for intervals determined by critical numbers and test in the first derivative F) Where derivative goes from negative to positive is a relative minimum, where the derivative goes from positive to negative there is a relative maximum. G) Where derivative goes from negative to positive is a relative maximum, where the derivative goes from positive to negative there is a relative minimum. If using the First Derivative Test 1) The first step would be [1] from the possibilities A through G listed above. 2) The second step would be [2] from the possibilities A through G listed above. 3) The third step would be [3] from the possibilities A through G listed above.

**Partial Credit Problem**  (4 points total) Determine the derivative of 

Match the functions from Z -> Z+ with its properties.