Graphing – an Application of the Derivative.

Graphing and the analysis of graphs given (1) the equation, (2) a graph, or (3) a table of values of a function and its derivative(s) makes up the largest group of questions on the AP exams. Most of the other applications of the derivative depend on understanding the relationship between a function and its derivatives.

Here is a list of posts on these topics. Since this list is rather long and the topic takes more than a week to (un)cover,

Tangents and Slopes

Concepts Related to Graphs

The Shapes of a Graph 

Open or Closed?  Concerning intervals on which a function increases or decreases.

Extreme Values


Joining the Pieces of a Graph

Using the Derivative to Graph the Function

Real “Real life” Graph Reading

Comparing the Graph of a Function and its Derivative  Activities on comparing the graphs using Desmos.

Writing on the AP Calculus Exams   Justifying features of the graph of a function is a major point-earner on the AP Exams.

Reading the Derivative’s Graph Summary and my most read post!




Revised from a post of October 10, 2017



2 thoughts on “Graphing – an Application of the Derivative.

  1. Hello,
    I’m not able to follow the links for using the derivative and writing on the ap exam.
    They take me to the page and ask to sign in.
    Thanks for all the great links and posts!


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