1. (10 pt) Find implicitly if . Check your answer by solving for and taking the derivative the "old fashioned way".

 

2. (7 pt) Find a polynomial that satisfies , , , and for .

 

3. (15 pt) An hourglass is shaped like an inverted circular cone with base radius 3 inches and height 6 inches. Sand pours out at 0.25 in³/min. How fast is the level of sand in the hourglass changing when the height of the sand left is 0.5 in?

 

4. (8 pt) Find the linearization of at the point (. Use this linearization to estimate sin(28° ).

 

5. (10 pt) Copy the following graph onto your paper. For the given starting point, illustrate the next two Newton’s Method approximations. Which root of f(x) (if any) do you think that Newton’s Method will "go to"?

 

 

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6. (25 pt) Find the derivatives of the following functions:

a) b) c)

d) e)

7. (15 pt) Mr. Burns is found dead in his mansion at 10 pm. His body temperature is measured and found to be 86° ^F. It is known that Chief Wiggam was at the mansion from 2-4pm, Mayor Quimby was there from 4pm-5pm, and Krusty the Clown was there from 5pm-6:30pm. If it took 15 minutes for Mr. Burns’ body temperature to drop 1° ^F from normal after he was killed and the mansion is kept at 80° ^F, who killed Mr. Burns?

8. (10 pt) Use inverse functions to show that.