Math 121 - Chapter 3 Study Guide




  1. For the accompanying position versus time graph, find the average velocity over an interval, the places where the instantaneous velocity is zero, the times at which the instantaneous velocity is a maximum or minimum, and the instantaneous velocity at a specific time. Look at problem 3.1.10.
  2. Match the graphs of the functions with the graphs of their derivatives. Five parts. Look at problem 3.2.23.
  3. Find the derivative. Five parts. Look at problems 3.3.1-28*.
  4. Find f'(x) for trigonometric functions. Four parts. Look at problems 3.4.1-18*.
  5. Find f'(x) using the chain rule. Four parts. Look at problems 3.5.1-39*.
  6. Find the derivatives as the specified point. Five parts. Look at supplementary exercise 3.10.
  7. Find dy/dx by implicit differentiation. Two parts. Look at problems 4.3.11-20*.
  8. Related rate problem. Look at problems 4.6.9-25*. Any formulas from geometry that you need are given on the exam.
  9. Use a local linear approximation to estimate the value given. Look at problems 3.6.27-35.
  10. Find the differential dy. Look at problems 3.6.9-12.
  11. Use the limit definition of the derivative (Definition 3.2.2) to find the derivative of the given function. Look at problems 3.2.9-14. Note: 9-14 ask for the equation of the tangent line, I'm just asking for the derivative. Also note that this is a problem where I will be grading work more than the answer. Be sure you write the limit in every time until you actually take the limit.
  12. True / false statements regarding continuity and differentiability of functions. Four parts.

Notes:

# 1 2 3 4 5 6 7 8 9 10 11 12 Total
Pts 8 5 15 16 16 10 8 5 4 4 5 4 100