Math Is Fun
Math Is Fun: Second Derivative
Second derivative description, examples, and interactive graphing.
Khan Academy
Khan Academy: Analyzing the Second Derivative to Find Inflection Points
Learn how the second derivative of a function is used in order to find the function's inflection points. Learn which common mistakes to avoid in the process.
Wolfram Research
Wolfram Math World: Second Derivative Test
MathWorld.com has definitions, formulas, and links to relevant sites for derivatives.
Harvey Mudd College
Harvey Mudd College: Concavity and the Second Derivative Test
An excellent tutorial explaining concavity and the second derivative test, including a labeled diagram, examples, and links to a quiz.
CK-12 Foundation
Ck 12: Using the First and Second Derivative Tests
[Free Registration/Login may be required to access all resource tools.] This resource gives a step by step account of how to apply knowledge from First and Second Derivative Tests to sketch graphs of functions. The following table...
Mathematics Archives
Math Archives: Visual Calculus: Graph a Function, Its Second Derivative
This online tutorial site shows that the concavity of a function is related to the second derivative of the function by using an online graphing system. Inflection points are also briefly discussed.
![Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 1 [Pdf] Unknown Type](https://static.lp.lexp.cloud/images/attachment_defaults/resource/large/FPO-knovation.png "Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 1 [Pdf] Unknown Type")
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 1 [Pdf]
Learners use the graph of the original function to sketch the graphs of the derivative and second derivative. The resource consists of an enlarged printable version of a math graph available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 2 [Pdf]
Learners use the graph of the original function to sketch the graphs of the derivative and second derivative. The resource consists of an enlarged printable version of a math graph available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 4 [Pdf]
Learners use the graph of the original function to sketch the graphs of the derivative and second derivative. The resource consists of an enlarged printable version of a math graph available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 5 [Pdf]
Learners sketch the graphs of the derivative and second derivative from the original function. The practice exercise is available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 6 [Pdf]
Learners sketch the graphs of the derivative and second derivative from the original function. The practice exercise is available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 7 [Pdf]
The practice exercise examines how to sketch the graphs of the derivative and second derivative from the original function. The example is available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 8 [Pdf]
The practice exercise examines how to sketch the graphs of the derivative and second derivative from the original function. The example is available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 11 [Pdf]
The handout asks learners to sketch the graphs of the derivative and second derivative. The resource consists of an enlarged printable version of a graph available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 12 [Pdf]
The handout asks learners to sketch the graphs of the derivative and second derivative. The resource consists of an enlarged printable version of a graph available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 13 [Pdf]
The handout investigates a sketch of a function?s derivative and second derivative. The exercise includes an enlarged printable version of the original function graph available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 14 [Pdf]
The handout investigates a sketch of a function?s derivative and second derivative. The exercise includes an enlarged printable version of the original function graph available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 15 [Pdf]
Students sketch the graphs of the derivative and second derivative of a given function. The example is available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 16 [Pdf]
Students sketch the graphs of the derivative and second derivative of a given function. The example is available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Function, Derivative, & Second Derivative 12 [Pdf]
Learners identify between a function graph, its derivative, and its second derivative. The graphs are available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Sketching Derivative & Second Derivative 3 [Pdf]
Learners use the graph of the original function to sketch the graphs of the derivative and second derivative. The resource consists of an enlarged printable version of a math graph available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Function, Derivative, & Second Derivative 11 [Pdf]
Learners identify between a function graph, its derivative, and its second derivative. The graphs are available in PDF format.
Math Graphs
Houghton Mifflin: Math Graphs: Second Derivative Graph 1 [Pdf]
A graph of the second derivative is given and learners are asked to sketch the graphs of the first derivative and original function. The handout is available in PDF format.