Curated OER
Inflection Points
In this inflection points worksheet, 11th graders solve and complete 5 different problems. First, they find intervals of x for which each of the following curves is increasing, decreasing, concave upward, concave downward. Then, students...
Curated OER
Polygons
In this polygons worksheet, 10th graders solve 18 various types of problems related to different forms of polygons. First, they state the number of sides for each convex polygon and then, use the polygon shown to respond to each of 6...
Curated OER
Worksheet 13: Slope and Concavity
In this function worksheet, students determine the equation of a line, compute slope and concavity of a graph, and find the maximum volume of three-dimensional figures. This one-page worksheet contains six multi-step problems.
Curated OER
Worksheet 6: Derivative & Slope
In this derivative and slope worksheet, students find the derivative of given equations. They identify the slope of a line tangent to a graph and find the concavity of a graph. This one-page worksheet contains seven multi-step problems.
Curated OER
Applications of Derivatives: Concavity and Optimization
In this derivatives worksheet, students sketch the graph of a function by determining the local maxima, minima and inflection points. They graph a second function when given the interval. Students solve two word problems involving...
Curated OER
Rate Equations, Slope Functions and Concavity
In this rate equation worksheet, students identify an inflection value for given functions. They determine an expression that stultifies a given rate equation. This three-page worksheet contains definitions, explanations and examples. ...
Curated OER
Comparison of Images Formed by Plane, Cylindrical (concave side), and Spherical (concave side) Mirrors
Students study mirrors and see how images can be reversed. In this reflection activity students demonstrate that all mirrors reverse images and that the apparent right to left reversal in a plane mirror is a result of that reversal.
Curated OER
Worksheet #5, Concavity,
For this calculus worksheet, students determine the intervals in which a given relation is concave up. They determine the inflection points of a given formula. Students use the second derivative test to classify the relative extrema of a...
Curated OER
Exploring the Landscape
Students determine the monotonicity and concavity properties of a function, then apply the First Derivative Test and draw conclusions about the first and second derivatives from these properties.
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.
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.
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.
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: Derivative Graph 1 [Pdf] Unknown Type](https://d15y2dacu3jp90.cloudfront.net/images/attachment_defaults/resource/large/FPO-knovation.png "Houghton Mifflin: Math Graphs: Derivative Graph 1 [Pdf] Unknown Type")
Math Graphs
Houghton Mifflin: Math Graphs: Derivative Graph 1 [Pdf]
Students 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.
Math Graphs
Houghton Mifflin: Math Graphs: Derivative and Second Derivative [Pdf]
Students use the graph of the derivative to approximate the slope, relative minimum, concavity, and inflection points. The exercise is available in PDF format.