Examine the mystery functions described below.
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 ________________________.
A different mystery function has all of the following properties:
, for , and for . Draw a sketch of 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 ___________________.