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3 Written questions

3 Multiple choice questions

  1. If f(x) is continuous in an interval [a, b] then somewhere on the interval it will achieve every value between f(a) and f(b); if f(a) is less than or equal to M, which is less than or equal to f(b), then there exists one value c in the interval [a, b] such that f(c) = M.
  2. [f(b) - f(a)] / (b-a)
  3. If the limit as h approaches zero of [f(a+h) - f(a)] / h exists, then the limit is differentiable at x=a. Notation: f'(a)

2 True/False questions

  1. Instantaneous Rate of ChangeHow fast f(x) is increasing or decreasing at the point x = a


  2. L'Hospital's RuleIf f(x) is continuous on the closed interval [a, b], differentiable on (a, b), and satisfies f(a) = f(b), then for some c in the interval (a, b), we have f'(c) = 0