Flipped Math
Calculus AB/BC - Using the Second Derivative Test to Determine Extrema
Take a second look at extrema of functions. Pupils learn how to use the second derivative to determine whether a critical point is a maximum or a minimum. Learners use concavity to identify critical points as either a max or a min and...
Curated OER
The Second Derivative Test for Relative Extreme in Three Dimensional Space
In this second derivative worksheet, students determine the relative maximum and minimum values of given surfaces in three-dimensional space. They perform the second derivative test, and identify the partial derivatives. This one-page...
Curated OER
Applications of Derivatives: Finding Maxima and Minima
In this derivative instructional activity, students use the second derivative test to determine the maxima and minima of given functions. They explore real life problems to complete the optimization of a problem. This two-page...
College Board
Vectors: A Curriculum Module for AP® Calculus BC
It is all in a matter of time. The model curriculum module uses parametric equations and vectors to solve problems dealing with particle motion along a curve. At the beginning of the lesson, the unit reviews parametric equations and...
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
A.P. Calculus Test Covering Limits, Derivatives, and Integrals
In this calculus worksheet, students solve ten multiple-choice questions and eleven free-response questions covering limits, derivatives, and integrals. Students should have covered trig limits prior to this worksheet.
Curated OER
The Second Derivative Test for Relative Extrema in Three Dimensional Space
For this math worksheet, students seek to find the relative maximum and minimum values of surfaces in three dimensional space for the function.
Curated OER
Practice Test for Midterm: Partial Derivatives
For this partial derivatives worksheet, students use Lagrange multipliers to find the maximum and minimum values of a given function. They find an equation of the tangent plane under given conditions and identify the second partial...
EngageNY
Construct a Square and a Nine-Point Circle
Anyone can draw a square, but can you CONSTRUCT a square? Here is a resource that challenges math scholars to create steps to finish their own construction. They test their ability to read and follow directions to complete a construction...
Curated OER
Finding the Extrema Graphically and Symbolically
In this extrema worksheet, students use the first derivative test and the second derivative test to determine the local extrema. They identify the local maximum and global maximum. This eight-page worksheet contains detailed...
Curated OER
Worksheet #5, Concavity,
In 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
Basic Calculus: Extrema, and Optimization: Putting it all Together
In this extrema and optimization worksheet, students identify all points in the domain and determine the critical points. They compute the second derivative and find the global maxima and minima. This two-page worksheet contains two...
EngageNY
Locating Ordered Pairs on the Coordinate Plane
Four quadrants, four times the fun. Future mathematicians learn the terminology associated with the coordinate plane and how to plot points in all four quadrants. A worksheet tests their understanding of the material in the 16th...
Curated OER
Curve Sketching
In this calculus worksheet, students sketch a curve using a given function. They take the derivative of a function and graph it. There are 10 questions.
Curated OER
AP Calculus
In this calculus learning exercise, students solve problems with trigonometric functions. They take the derivative and find the average rate of change.
Curated OER
Sixteen Multiple Choice AP Calculus AB Exam Practice Questions
In this AP Calculus AB Exam worksheet, students answer sixteen multiple choice questions in preparation for the AP Exam. These questions include many topics covered on the exam.
Curated OER
Curve Sketching
In this calculus worksheet, students 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.
EngageNY
Ruling Out Chance (part 3)
Pupils analyze group data to identify significant differences. They use simulation to create their own random assignment data for comparison.
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...
Wolfram Research
Wolfram Math World: Second Derivative Test
MathWorld.com has definitions, formulas, and links to relevant sites for derivatives.
Math Is Fun
Math Is Fun: Second Derivative
Second derivative description, examples, and interactive graphing.
Varsity Tutors
Varsity Tutors: Hotmath: Practice Problems: Applications of Derivatives
Hotmath provides 25 practice problems dealing with derivative applications. Each of the practice problems include a step-by-step guide.