Section 2.3 – The Derivative Function Section 2.3.1 – The Graph of the First Derivative Function.

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Presentation transcript:

Section 2.3 – The Derivative Function Section – The Graph of the First Derivative Function

This is the graph of f(x). This is the graph of f ‘ (x). How do we get this? f(x) inc f ‘ (x) pos f(x) dec f ‘ (x) neg

This is the graph of f(x). This is the graph of f ‘ (x).

Steps to Graphing The First Derivative 1. Graph the x-intercepts (slope of tangent is zero) 2. Mark points of inflection (opening up/down changes) 3.Analyze trends of slopes and fill in shapes. Note: the y-axis of the derivative graph is no longer a y-coordinate, but a VALUE OF SLOPE

Example of Graphs of First Derivative

This is the graph of f(x) Graph f ‘ (x).

Section – The Derivative Function

Use the results to sketch a graph of f ‘ over the interval [0, 3]