Section 2.3 – The Derivative Function

Section 2.3.1 – 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) incf ‘ (x) pos

f(x) decf ‘ (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).