Develop, explain, and apply strategies for finding higher order derivatives and their notations.

Develop, explain, and apply strategies for using the first derivative to determine:

• critical points
• increasing and decreasing intervals.

Develop, explain, and apply strategies for using the second derivative to determine:

• points of inflection
• concavity intervals.

Describe the difference between relative and absolute extrema.

Apply the first and second derivatives to determine relative and absolute extrema.

Analyze graphical representations of $f(x)$ to identify critical point(s), increasing and decreasing intervals, point(s) of inflection, and concavity intervals.

Identify characteristics of $f(x)$ when given the graph of the first derivative and/or second derivative.

Identify characteristics of $f(x)$ when given descriptions of the first derivative and/or second derivative.

Apply understanding of limits to determine vertical and horizontal asymptotes.

Sketch the graph of a function with and without the use of technology.

Critique the statement, “An absolute maximum or minimum value occurs at $x=a$, if and only if $f'(a) = 0$.”