Finding Extrema

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After completing this section, students should be able to do the following.

Find and classify local extrema of a function using derivatives.
Evaluate local extrema of a function to determine their values.
Apply the extreme value theorem to determine that functions have absolute extrema.
Identify when a function can and cannot have EVT applied to it.
Correctly locate and classify absolute extrema.
Determine if a function has absolute extrema.
Use the second derivative to classify critical values as the correct extrema type.
Identify when the second derivative test succeeds, and when it fails.
Correctly interpret what the failure of the second derivative test means.