Math 121 - Final Exam Study Guide

1. Express the function in piecewise form without using absolute values.
2. Sketch the curve by eliminating the parameter, and indicate the direction of increasing t.
3. The graph of a function is given. Sketch the graph of its derivative.*
4. Find the limit. Show any work necessary. Nine parts.
5. Find the derivative. Six parts.
6. Use the values of the functions and their derivatives given in the table to find the indicated derivatives.
7. Find dy/dx by implicit differentiation.
8. Use the accompanying graph to find the intervals where f is increasing, decreasing, concave up, concave down, and indicated any inflection points.
9. Find the absolute maximum and minimum on the closed interval.
10. Sketch the region enclosed by the curves and find its area.
11. The position function of a particle moving along a coordinate line is given. Find the velocity and acceleration; evaluate the position, velocity, speed, and acceleration at a specific instant; identify when the particle is stopped, speeding up, and slowing down; find the total distance traveled by the particle.
12. Evaluate the integral. Six parts.
13. Sketch the region and find the volume of the solid that results when the region enclosed by the given curves is revolved about the indicated axis. Identify the method you are using.
14. Find the fluid force against a submerged surface.
15. Find a function that has a relative minimum and maximum at the indicated x-values and the given y-intercept.* Hint: Start with what has to be true for an extremum to occur and work backwards to the function.
16. Related rate application problem.
17. Give a complete graph of the polynomial and label the coordinates of the intercepts, stationary points, and inflection points. Check your work with a graphing utility.
18. One of each pair of statements is correct, circle the letter of the correct statement. Thirteen parts. These come from all parts of the course and should be pretty obvious if you've learned the material.

Notes:

• Problems are similar to problems off of old exams with the exception of the *'d problems.