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Multiple Choice: Let be the function given by . Which of the following statements about are true?

  1. is continuous at .

  2. is differentiable at .

  3. has an absolute minimum at .

Examples of functions that are not differentiable at . Notice that some of them are still continuous at .

The Three Conditions of Continuity

  1. I only

  1. II only

  1. III only

  1. I and III

  1. II and III