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First derivative test for local extrema

Author:Tim Brzezinski
The First Derivative Test for Local Extrema states that if is a critical point of a continuous function , and if is differentiable at every point in some interval containing except possibly at itself, then
  1. If changes from negative to positive at , then has a local minimum at .
  2. If changes form positive to negative at , then has a local maximum at .
  3. If does not change sign at , then has no local extremum at .
Drag the black point along the graph of function . As you do, its derivative and local extrema will appear. Notice how has no local extremum at the first black point that appears on the function. Why is this?
Developed for use with Thomas' Calculus, published by Pearson.

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