# AP Calculus final

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1. critical point
or undefined
2.    or undefined
critical point
3. inc function f(x)
f'>0
4. f'>0
inc function f(x)
5. dec function f(x)
f'<0
6. f'<0
dec function f(x)
7. concavity inc slope
f''>0
8. f''>0
concavity inc slope
9. concavity dec slope
f''<0
10. f''<0
concavity dec slope
11. local minimum
goes (-,0,+) or (-,DNE,+) or
12.   goes (-,0,+) or (-,DNE,+) or
local minimum
13. local maximum
goes (+,0,-) or (+,DNE,-) or
14.   goes (+,0,-) or (+,DNE,-) or
local maximum
15. point of inflection
• f''=0 or DNE and concavity changes
•   goes from (+ to -), (- to +)
16. f''=0 or DNE and concavity changes
goes (+ to -),(- to +)
point of inflection
17. abs. max/min
eval. crit# & endpoints or discuss "always inc or always dec"
18. eval. crit# & endpoints or discuss "always inc or always dec"
abs. max/min
19. intermediate value theorem
• if the function f(x) is continuous on [a,b], for all k between f(a) and f(b), there exists at least one number x=c in the open interval:
• (a,b) such that f(c)=k
20. if the function f(x) is continuous on [a,b], for all k between f(a) and f(b), there exists at least one number x=c in the open interval:(a,b) such that f(c)=k
intermediate value theorem
21. extreme value theorem
if the function f(x) is continuous on [a,b], then there exists an absolute max and min on that interval
22. if the function f(x) is continuous on [a,b], then there exists an absolute max and min on that interval
extreme value theorem
23. Rolle's theorem
• if the function f(x) is continuous on [a,b], AND
• differential on the interval (a,b), AND
• f(a)=f(b), then there is at least on number
• x=c in (a,b) such that f'(c)=0
24. if the function f(x) is continuous on [a,b], ANDdifferential on the interval (a,b), ANDf(a)=f(b), then there is at least on numberx=c in (a,b) such that f'(c)=0
Rolle's theorem
25. mean value theorem
• If the function f(x) is continuous on [a,b], AND
• differential on the interval (a,b), then
• there is at least one number x=c in (a,b)
• such that

26. If the function f(x) is continuous on [a,b], AND
differential on the interval (a,b), then
there is at least one number x=c in (a,b)
such that
mean value theorem
27. MVT of Integrals i.e. AVERAGE VALUE
• If the function f(x) is continuous on [a,b] and differential on the interval (a,b), then there exists at least one number x=c on (a,b) such that

This value f(c) is the "average value" of the function on the interval [a,b].
28. If the function f(x) is continuous on [a,b] and differential on the interval (a,b), then there exists at least one number x=c on (a,b) such that

This value f(c) is the "average value" of the function on the interval [a,b].
MVT of Integrals i.e. AVERAGE VALUE
29. Limit Strategies
• Factor and cancel, rationalize numerator, u-sub HA rules:

30. Factor and cancel, rationalize numerator, u-sub HA rules:

Limit Strategies
31. To find all HA
Take limit as
32. Take limit as
To find all HA
33. Approximation methods for integration
Rectangles
Left, right and middle Riemann sums A=bh
34. Left, right and middle Riemann sums A=bh
• Approximation methods for integration
• Rectangles
35. Approximation methods for integration
Trapezoids
• Approximation methods for integration
• Trapezoids
36. Effects of inc/dec & concavity on approximation
Concave up
M under estimate, T over estimate
37. Effects of inc/dec & concavity on approximation Concave down
M over estimate, T under estimate
38. Effects of inc/dec & concavity on approximation
inc
L=under, R=over
39. Effects of inc/dec & concavity on approximation
dec
L=over,R=under
40. First fundamental theory of calculus
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41. First fundamental theory of calculus
42. Second fundamental theory of calculus
43. Second fundamental theory of calculus
44. disk method
45. disk method
46. washer method
47. washer method
48. volume by cross section (not rotated)

49. Volume by cross section (not rotated)
50. Velocity
51. Velocity
52. Acceleration
53. Acceleration
54. Displacement
55. Displacement
56. total distance
57. total distance
58. Average velocity
59. Average velocity
 Author: Sbjohnson ID: 302889 Card Set: AP Calculus final Updated: 2015-05-18 05:04:44 Tags: Calculus Folders: Description: AP Calculus final flashcards Show Answers: