**MATH 2431 – Summer
Session 2005**

**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.