Essential Understanding 2.2

Essential Understanding 2.2 Students will understand that a function's derivative, which is itself a function, can be used to understand the behavior or the function.

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Learning Objective 2.2A Students will be able to use derivatives to analyze properties of a function.

Essential Knowledge 2.2A1 Students will know that first and second derivatives of a function can provide information about the function and its graph including intervals of increase or decrease, local (relative) and global (absolute) extrema, intervals of upward or downward concavity, and points of inflection.

Essential Knowledge 2.2A2 Students will know that key features of functions and their derivatives can be identified and related to their graphical, numerical, and analytical representations.

Essential Knowledge 2.2A3 Students will know that key features of the graphs of f, f ', and f '' are related to one another.

Learning Objective 2.2B Students will be able to recognize the connection between differentiability and continuity.

Essential Knowledge 2.2B1 Students will know that a continuous function may fail to be differentiable at a point in its domain.

Essential Knowledge 2.2B2 Students will know that if a function is differentiable at a point, then it is continuous at that point.