# 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

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

Extreme Values

Concavity

Joining the Pieces of a Graph

Using the Derivative to Graph the Function

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.

Revised from a post of October 10, 2017

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

1. Davis Searl says:

Hello,
I’m not able to follow the links for using the derivative and writing on the ap exam.
• Lin McMullin says: