MATH 2431 – Summer Session 2005

TEST 2

NAME_______________________________________________________

You may NOT use a calculator on this portion of the test. Show work and write clearly.

1. (10 points) Find the first derivative: .

2. (10 points) Find the first AND second derivatives: .

3. (10 points) Find the intervals of increase/decrease: .

4. (10 points) Find the intervals of concavity: .

5. (10 points) Find the critical points and inflection points: .

6. (10 points) Find the equation of the tangent line to f(x) at x = 0: .

7. (10 points) Use the limit definition to find the derivative of .

8. (10 points) Given . Use the linear approximation for f(x) at x = 2 to

estimate f(x) for x = 1.98 and x = 2.3.
NAME_______________________________________________________

You may NOT use a calculator on this portion of the test. Show work and write clearly.

9. (10 points) Consider the slope of the curve at each of the five points shown. List these five slopes in increasing order and explain your reasoning.

.

10. (10 points) The figure below shows the graphs of , ,  and . Identify each curve and explain your choices.