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Math 1A
·
Module 6
Analyzing Functions with Derivatives
1
Rolle's and Mean Value Theorems
Apply Rolle’s Theorem and the Mean Value Theorem to relate average and instantaneous rates of change.
2
First Derivative Test: Increasing/Decreasing Functions and Local Extrema
Use the First Derivative Test to determine where a function is increasing or decreasing and to find local extrema.
Second Derivative Test: Concavity and Inflection Points
Use the Second Derivative Test to determine the concavity of a function and locate inflection points.
4
Classifying Extrema with the Second Derivative Test
Apply the Second Derivative Test to classify local extrema.
5
Sketching Curves Using Derivatives
Sketch the graph of a function by combining information from the function, its first derivative, and its second derivative.
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