(Question 3) 8 points A Folium of Descartes is the family of curves given by

(Question 4) 8 points Sketch a possible graph for a continuous function  that has ALL the stated conditions.  Label your graph. The domain of is the interval

(Question 9) 8 points Graph of the position function of a particle is shown, where t is measured in seconds.     a. When the particle is speeding up ? (Enter your answers using interval notation.)   b. When the particle is slowing down ? (Enter your answers using interval notation.)  

(Question 6) 12 points (a) On what intervals is f increasing ? (Enter your answer using interval notation.) (b) On what intervals is f decreasing ? (Enter your answer using interval notation.) (c) At what value(s) of x does f have a local maximum ? (Enter your answers as a comma-separated list.) (d) On what interval(s) is f concave upward? (Enter your answer using interval notation.)

(Question 5) 12 points Sketch a possible graph for a function  that has ALL the stated conditions.  Label your graph.   ,

(Question 3) 6 points Suppose

(Question 7) 15 points Suppose is a positive real number and that

(Question 1) 6 points Suppose A is a nonzero real number.  Evaluate the following limit, if possible.  If the limit does not exist, explain why not.

(Question 2) 9 points Suppose that  is continuous at and that

(Question 8) 12 points The population, , in thousands, of a certain city is given by where t is the number of years since .  At what average rate does the population change from to ? Include correct units. Find . What does this value represent in the context of this problem?  Include correct units.