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Examine the mystery functions described below.

  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.

    means that there COULD be a local maximum or local minimum at .
    means that is concave down at , confirming that 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 ___________________.