1. (10 pt) Find the tangent line to the graph of y³x+x²y=2 at the point (-2,1).

2. (10 pt ) Consider the function . Show the function is one to one, and compute its inverse function.

3. (10 pt ) Let . Let be the inverse function of , compute

4. (5 pt ) Estimate by using the linearization of at 32.

5. (30 pt ) Compute the following derivatives:

a) d)

b) e)

c) f)

6. (5 pt ) Sketch the graph of

7. (10 pt ) Sand is being dumped into a pile at a rate of 100 cubic meters per minute. The pile is such that its radius is always equal to its height. How fast is the height of the pile increasing when it is 5 meters high? (Hint: Volume of a cone is one third of the base times the height).

8. (10 pt ) Consider the following function:

For the initial approximations listed, which root of the function (if any) will Newton’s method find? Justify your answer.

9. (10 pt ) A bacteria colony starts with 100 bacteria and doubles in size every 2 hours. Find a formula for the number of bacteria in the colony at any time.