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Examine the mystery functions described below. Homework Help ✎

  1. has all of the following properties:  , , and. Assuming the function is continuous, sketch a small portion of the mystery function near . Describe the function at this point.

    f '(2) = 0 means that there COULD be a local maximum or local minimum at x = 2.
    f ''(2) < 0 means that f(x) is concave down at x = 2, confirming that x = 2 is a local ________________________.

  2. A different mystery function has all of the following properties: , for , and for . Sketch near and state a conclusion.

    If slope is positive on the left side of a point and negative on the right side, the that point is the location of a local ___________________.