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5 Written Questions

5 Matching Questions

  1. Fundamental Theorem of Calculus #1
  2. Antiderivative of xⁿ
  3. -cot(x)+C
  4. Derivative of ln(u)
  5. Cubing function
  1. a
    D: (-∞,+∞)
    R: (-∞,+∞)
  2. b
  3. c
  4. d
  5. e
    The definite integral of a rate of change is the total change in the original function.

5 Multiple Choice Questions

  1. If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical points in the interval or at endpoints of the interval.

  2. This is a graph of f'(x). Since f'(C) exists, differentiability implies continuouity, so Yes.
    Yes f' decreases on X<C so f''<0
    f' increases on X>C so f''>0
    A point of inflection happens on a sign change at f''

  3. D: (-∞,+∞)
    R: (0,+∞)

5 True/False Questions

  1. 0


  2. -csc²(x)


  3. Formula for Disk Method
    Axis of rotation is a boundary of the region.


  4. nx^(n-1)


  5. First Derivative Test for local extrema


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