Concavity and the Second Derivative Test

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

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 and second derivatives.
Sketch a graph of a function satisfying certain constraints on its higher-order derivatives.
State the relationship between concavity and the second derivative.
State the Second Derivative Test.
Apply the Second Derivative Test.
Define inflection points.
Find inflection points.