Curated OER
Curve Sketching
In this calculus worksheet, learners identify the point of increase and decrease on a graph. They analyze the curve of a graph using the derivative. There are 10 open questions about derivatives.
Cuemath
Cuemath: Concave Shapes
A comprehensive guide for learning all about concave shapes with definitions, the difference between concave and convex, examples, and practice questions.
Khan Academy
Khan Academy: Analyze Concavity
Find intervals where a function (given algebraically) is concave up or down.
Khan Academy
Khan Academy: Algebra I: Compare Quadratic Functions
Compare the properties of two quadratic functions, each represented in a different way. Students receive immediate feedback and have the opportunity to try questions repeatedly or receive hints.
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.
Other
Representacion Grafica De Funciones
In Spanish. In depth explanations of functions at an advanced level. Includes topics such as concavity, points of inflection and relative maximums and minimums. A great resource for the Spanish speaking student to keep up in the English...
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...
Physics Classroom
The Physics Classroom: Refraction and the Ray Model of Light: Anatomy of a Lens
Illustrated diagrams in this tutorial help students understand the properties and functions of lenses.
Ministry of Education and Universities of the Region of Murcia (Spain)
Ministerio De Educacion Y Ciencia: Aplicaciones De La Derivada
In Spanish. In this interactive unit learn how to calculate intervals of growth and decay, maximum and minimum value of a function, the intervals of concavity and convexity and the turning points of a function.
Cuemath
Cuemath: Convex Shapes
A comprehensive guide for learning all about convex shapes with definitions, examples, and practice questions.
Math Graphs
Houghton Mifflin: Math Graphs: Derivative Graph 1 [Pdf]
Learners use the graph of the derivative to answer questions regarding the original function. Maximum, minimum, concavity, and slope are investigated. The handout is available in PDF format.
Texas Instruments
Texas Instruments: Graphing Relationships
In this activity, students explore information about a graph based on the first and second derivatives. They learn that a function's derivative is positive when the function increases and negative when the function decreases. They learn...
Other
Ctte: Geometer's Sketch Pad Activities
This site offers numerous activities for middle school and high school students to explore using Geometer's Sketch Pad.