FTCE Math Review Deck 2

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  1. What are 5 conditions in which f(x) does not have a derivative at x = c?
    • 1.  f(x) is discontinuous at x=c.
    • 2.  f(x) has a vertical tangent at x=c.
    • 3.  f(x) has a cusp at x=c.
    • 4.  f(x) has a corner at x=c.
    • 5.  f(x) has a vertical asymptote at x=c.
  2. For a rational function Image Upload, if the degree of p(x) > degree of q(x), then Image Upload
    0
  3. For a rational function Image Upload, if the degree of p(x) = degree of q(x), then Image Upload
    k, where k=ratio of the p and q's leading coefficients
  4. For a rational function Image Upload, if the degree of p(x) < degree of q(x), then Image Upload
    Image Upload, which is also interpreted that the limit does not exist
  5. The average rate of change over an interval is equal to __________.
    the slope of the secant line
  6. The instantaneous rate of change at any point is equal to _____________.
    the slope of the line tangent to the point.
  7. Image Upload
    Image Upload
  8. Image Upload Image Upload
    Image Upload
  9. Image Upload
    Image Upload
  10. What is a critical point on a graph?
    a place where the derivative is 0 or is undefined
  11. Any point on the graph at which the first derivative is zero represents a ____________.
    minimum or maximum
  12. To determine if a critical point is a maximum or minimum you should __________.
    evaluate two points Image Upload and Image Upload and compare the change in slope
  13. The first derivative measures ________.
    The second derivative measures __________.
    • the slope of the function
    • the change in the slope of the function (concavity)
  14. If Image Upload, g(x) is concave ______.
    upward
  15. If Image Upload, then g(x) is said to be concave ________.
    downward
  16. The points of inflection are where the first derivative _____________.
    changes sign (negative to positive or positive to negative)
  17. Using the 2nd Derivative Test:
    f(x)        f'(x)       f''(x)
    ?            =0         >0
    ?            =0         <0
    ?            =0         =0
    • min
    • max
    • no determination can be made
  18. Image Upload
    Image Upload
  19. Image Upload
    Image Upload
  20. Image Upload
    Image Upload
  21. Image Upload
    Image Upload
  22. Image Upload
    Image Upload
  23. Image Upload
    Image Upload
  24. Image Upload
    Image Upload
  25. Fundamental theorem of calculus:
    Image Upload
    F(b) - F(a)
  26. For a portion of a function lying below the x-axis in range [c,d], find the area by calculating:
    Image Upload
  27. To find the area between 2 curves:  
    Area = ?
    • Image Upload
    • where:
    • f(x) is the top/right curve
    • g(x) is the bottom/left curve
  28. The symbol Image Upload means _________.
    • Union
    • Image Upload B = in A, in B, or in both
  29. The symbol Image Upload means _______.
    • intersection
    • Image Upload B = elements A and B have in common
  30. The symbol Image Upload means _______.
    subset
  31. The symbol Image Upload means _______.
    is an element of
Author:
akrell
ID:
232594
Card Set:
FTCE Math Review Deck 2
Updated:
2013-09-03 18:24:32
Tags:
calculus trig math
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Description:
Second set of review cards for the Florida Teacher Certification Exam in Mathematics (grades 6-12)
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