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AB Calc Final Exam Test

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3 Written Questions

3 Multiple Choice Questions

  1. Suppose 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).
  2. A generalization of Rolle's Theorem. If f(x) is continuous on the closed interval [a, b], differentiable on (a, b), then there exists one c on (a, b) such that f'(c) = [f(b) - f(a)] / (b-a)
  3. 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 True/False Questions

  1. Intermediate Value TheoremA generalization of Rolle's Theorem. If f(x) is continuous on the closed interval [a, b], differentiable on (a, b), then there exists one c on (a, b) such that f'(c) = [f(b) - f(a)] / (b-a)

          

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

          

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