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3 Written questions

3 Multiple choice questions

  1. If 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
  2. 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.
  3. How fast f(x) is increasing or decreasing at the point x = a

2 True/False questions

  1. Definition of DerivativeIf the limit of f(x) as x approaches a exists, and the limits are equal to f(a) at the point and from both sides, then f(x) is continuous at x=a


  2. L'Hospital's RuleSuppose two functions f(x) and g(x) are differentiable around a and g'(x) does not equal zero, Then iff trying to find the limit as x approaches a of f(x)/g(x) and the limit of f(x) and g(x) both equal zero, or both equal infinity, then the limits of indeterminate form can be evaluated by taking the derivative of both f(x) and g(x).


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