Concepts of Calculus Objectives
 Given two functions, find a rule for the sum, difference, product, quotient or composition of the
functions. (2.2:1-30)
 Given a function, find two functions whose composition yields the given function
(2.2:35-42)
 Given a function, evaluate the difference quotient. (2.2:38-42)
 Evaluate an expression involving limits (2.4:17-62)
 Evaluate an expression involving one-sided limits. (2.5: 21-42)
 Given a function, identify intervals over which the function is continuous. (2.6:51-66)
 Given a demand equation and a supply equation, find the equilibrium quantity and price.
(2.3; 51-56)
 Given a function, apply rules of differentiation to find the derivative. (3.1:1-34, 3.2:1-30; 3.3:1-46)
 Given a point of a given function, write an equation of the line tangent to the graph of the function at
that point. (3.1:41-44, 3.2:39-42, 3.3:59-62, 3.6:31-34, 5.4:33-34; 5.5:47-48)
 Use the cost function to find the actual and marginal cost of manufacturing the nth unit.(3.4: 2-3)
 Given the cost function, determine the average cost function and marginal average cost
function.(3.4:5, 14,15)
 Given a demand equation, determine the revenue function.(3.4:9)
 Given the revenue and cost functions, determine the profit function. (3.4:11a)
 Determine the marginal cost, marginal revenue and marginal profit functions. (3.4:10-13)
 Given a demand equation, determine and interpret the elasticity of demand. (3.4:22-33)
 Determine higher order derivatives of a function. (3.5:1-28)
 Interpret the results of a problem involving derivatives.
 Perform implicit differentiation on an equation. (3.6: 9-30)
 Solve a problem using related rates. (3.6:39-60)
 Find the differential of a given function. (3.7:1-14)
 Use differentials to solve application problems. (3.7:19-35)
 Given a function (graph or equation) determine the interval(s) where the function is increasing and
decreasing. (4.1:10-35; 5.4:35-36; 5.5:49-50)

Given a function (graph or equation) determine any relative maxima or minima. (4.1:48-71)
 Given a function determine interval(s) where the function is concave upward and concave downward.
(4.2:22-43; 5.4: 37-38; 5.5:51-52)
 Given a function determine any inflection points. (4.2: 44-55; 5.4:39-40; 5.5:53-54)
 Given a function (including exponential and logarithmic). (4.3, 5.1, 5.2)
o Determine the domain
o Identify x- and y- intercepts
o Identify horizontal and vertical asymptotes
o Identify intervals where it is increasing or where it is decreasing.
o Determine the relative maxima and relative minima, if any.
o Identify intervals where the function is concave upward and where it is concave downward.
o Determine inflection points, if any.
o Use the above properties to sketch the graph of the function
 Find the absolute extrema of a function. (4.4:9-38; 5.5:55-56)
 Apply the Laws of Exponents to expressions. (5.1: 1-16)
 Solve an exponential equation when the bases can be equated. (5.1:17-26)
 Apply the Laws of Logarithms to expressions. (5.2:17-26)
 Use logarithms to solve exponential equations (5.2:33-42)
 Solve problems involving compound interest (5.3)
 Given a nominal rate and the number of conversions per year, determine the effective rate. (5.3:5,6)
 Use logarithmic differentiation (5.5:37-56)
 Given a function containing powers of e or logarithms, find the derivative (5.4:1-28;
5.5:1-32)
 Find the antiderivative of a function (indefinite integral)
using the basic rules (6.1:9-50)
by substitution (6.1:1-50)
 Given the derivative of a function and an initial value of the function, find the function.
(6.1:51-58, 6.2:51-54)
 Find the area of a region under a graph on a given interval. (6.4:5-16)
 Evaluate a definite integral. (6.4:17-40; 6.5:1-28)
 Find the average value of a function over a given interval. (6.5:29-38)




Find the area between two curves in a given interval. (6.6:17-26)
Find the area of a region enclosed by two graphs. (6.6:35-40)
Solve problems involving consumers' surplus and producers' surplus (6.7:1-7)
Solve problems involving applications of any of the above.
Practice Problems (Most are from Chapter Reviews. Answers are in the back of the book,)
1. page 180:5
14. page 275: 43
27. page 370: 27
40. page 437: 41
2. page 180:7
15. page 275: 45
28. page 370: 29
41. page 544: 3
3. page 180:13
16. page 275: 49
29. page 370: 33
42. page 544: 5
4. page 180:15
17. page 275: 51
30. page 370: 35
43. page 544: 9
5. page 180:19
18. page 259: 41
31. page 370: 37
44. page 544: 19
6. page 180:21
19. page 260: 61
32. page 437: 5
45. page 544: 23
7. page 181:33
20. page 272: 39
33. page 437:11
46. page 545: 29
8. page 181:37
21. page 369: 1
34 page 437: 15
47. page 545: 31
9. page 274: 3
22. page 369: 5
35. page 437: 21
48. page 545:33
10.page 274: 13
23. page 369: 19
36. page 437: 27
49. page 545: 39
11.page 274: 17
24. page 369:21
37. page 437: 33
50. page 545: 43
12.page 275:35
25. page 370: 23
38. page 437: 35
51. page 546: 45
13.page 275: 37
26. page 370: 25
39 page 437: 39
52. page 546: 53
53. page 546: 55
Bring to the exam:
 Student ID
 Your Approved Graphing Utility
Final Exam
Monday May 3, 2004
7:45am – 9:55am
Location: CBA 121