4.3 how dx affect shape of graph

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jojobean0203
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215009
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4.3 how dx affect shape of graph
Updated:
2013-04-22 03:11:18
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calc
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how dx affect shape of graph
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  1. inflection point
    • any value of x where concavity changes
    • more formally, point P on y = f(x) if f(x) is continuous @ that point if curve changes from CU to CD or from CD to CU @ P
  2. increasing/decreasing test
    • f'(x) is +: f(x) is increasing
    • f'(x) is - : f(x) is decreasing
  3. first dx test
    • local max @ c: if f'(x) changes from + to - @ c
    • local min @ c: if f'(x) changes from - to + @ c
    • none @ c:  if f'(x) does not change sign @ c
  4. concave upward
    if graph of f(x) lies above all its tangents on an interval I
  5. concave downward
    if graph of f(x) lies below all its tangents on an interval I
  6. second dx test helps determine
    • * intervals of concavity
    • * max & min values
  7. concavity test
    • concave up on I:  f"(x) + for all x in I
    • concave down on I: f"(x) - for all x in I
  8. second dx test
    • f"(x) is continuous near c
    • local max @ c: if f'(c) = 0 & f"(c) +
    • local min @ c: if f'(c) = 0 & f"(c) -
  9. inconclusive second dx test
    • when f"(c) = 0 or when f"(c) dne
    • max, min, or neither
  10. T/F:
    if f'(x) is increasing, f(x) is +
    if f'(x) is decreasing, f(x) is -
    F: inverse/backwards

    • correct:
    • if f(x) is increasing, f'(x) is +
    • if f(x) is decreasing, f'(x) is -
  11. T/F:
    if f(x) is increasing, f'(x) is +
    if f(x) is decreasing, f'(x) is -
    T
  12. What does f'(x) say about f(x)?
  13. What does f"(x) say about f(x)?

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