Derivative Applications – Graphing

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, I will leave it as the lede post for the next two weeks.

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!







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