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5 Written Questions

5 Matching Questions

  1. Antiderivative of f(x) from [a,b]
  2. Inverse Secant Antiderivative
  3. sin(x)+C
  4. Rolle's Theorem
  5. sec²(x)
  1. a Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).
  2. b
  3. c
  4. d
  5. e

5 Multiple Choice Questions

  1. 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. ln(x)+C


  2. Alternative Definition of a Derivative


  3. f is continuous at x=c if...


  4. sec(x)tan(x)


  5. Identity function
    D: (-∞,+∞)
    R: (-∞,+∞)


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