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5 Written questions

5 Matching questions

  1. Intermediate Value Theorem
  2. Fundamental Theorem of Calculus #1
  3. ln(cscx+cotx)+C = -ln(cscx-cotx)+C
  4. Square root function
  5. First Derivative Test for local extrema
  1. a
  2. b If f is continuous on [a,b] and k is a number between f(a) and f(b), then there exists at least one number c such that f(c)=k
  3. c
    D: (0,+∞)
    R: (0,+∞)
  4. d
    The definite integral of a rate of change is the total change in the original function.
  5. e

5 Multiple choice questions

  1. D: (-∞,+∞)
    R: [0,+∞)

  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''

5 True/False questions

  1. Fundamental Theorem of Calculus #2


  2. ln(sinx)+C = -ln(cscx)+C


  3. Critical NumberIf f'(c)=0 or does not exist, and c is in the domain of f, then c is a critical number. (Derivative is 0 or undefined)


  4. f is continuous at x=c if...
    D: (-∞,+∞)
    R: (-∞,+∞)


  5. Mean Value Theorem
    The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line.