AP Calculus final

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  1. critical point
    Image Upload   or undefined
  2. Image Upload   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
    Image Upload  goes (-,0,+) or (-,DNE,+) or Image Upload
  12. Image Upload  goes (-,0,+) or (-,DNE,+) or Image Upload
    local minimum
  13. local maximum
    Image Upload  goes (+,0,-) or (+,DNE,-) or Image Upload
  14. Image Upload  goes (+,0,-) or (+,DNE,-) or Image Upload
    local maximum
  15. point of inflection
    • f''=0 or DNE and concavity changes
    • Image Upload  goes from (+ to -), (- to +)
  16. f''=0 or DNE and concavity changes
    Image Upload  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
    • Image Upload
    • 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 Image Upload
  26. Image Upload
    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 Image Upload
    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
    • Image Upload

    Image Upload

    Image Upload

    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
    Image Upload

    Image Upload

    Image Upload

    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:
    • Image Upload

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

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


    Image Upload
  50. Image Upload


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