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,
Open or Closed? Concerning intervals on which a function increases or decreases.
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
Teaching Calculus 
Hello,
I’m not able to follow the links for using the derivative and writing on the ap exam.
They take me to the WordPress.com page and ask to sign in.
Thanks for all the great links and posts!
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Davis – Thank you. I’m just organizing this page and some others. I have fixed the links and you should be able to get to the right places now.
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