Higher order derivatives and graphs

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

Use the first derivative to determine whether a function is increasing or decreasing.
Define higher order derivatives.
Compare differing notations for higher order derivatives.
Identify the relationships between the function and its first and second derivatives.
Sketch a graph of the second derivative, given the original function.
Sketch a graph of the original function, given the graph of its first or second derivative.
Sketch a graph of a function satisfying certain constraints on its higher-order derivatives.
State the relationship between concavity and the second derivative.
Interpret the second derivative of a position function as acceleration.
Calculate higher order derivatives.
Given the graph of a position function, find time intervals where the velocity is positive/negative
Given the graph of a position function, find time intervals where the velocity is increasing/decreasing