Curated OER
River Optimization Problem
Students define the different methods used for optimizing a particular element of a problem. In this optimization problem lesson, students optimize appropriate details of a problem using data collection, algebra, technology, and/or...
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
Finding Extrema Graphically and Symbolically
In this extrema worksheet, students use graphing calculators and the optimization method to identify the maximum and minimums of a given function. They compute the first and second derivative, and graph the functions. This eight-page...
Curated OER
Basic Calculus: Extrema, and Optimization: Putting it all Together
For 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...
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
Multivariable Calculus: Extrema of Multivariable Functions
In this multivariable function worksheet, students determine the extrema of multivariable functions, classify critical points, and solve functions with given boundaries. This two page worksheet contains five multi-step problems as well...
Curated OER
Multivariable Calculus: Extrema of Multivariable Functions
For this multivariable functions worksheet, students find the extrema of a function under given conditions. They find the maximum and minimum values of functions. This two page worksheet contains examples, explanations, and five problems.
Curated OER
Math 155 - Worksheet 13. Intervals
In this interval worksheet, students find the intervals of increase and decrease and all local extrema. They sketch a graph of the function and describe the intervals of concavity and all inflections points. This two-page worksheet...
Curated OER
Worksheet 22-Fall 1995
In this math activity, students examine the graph of the derivative. Then they determine the critical points that correspond to the relative extrema.
Harvey Mudd College
Harvey Mudd College: First Derivative Maxima and Minima
Shows how to find absolute extrema using the first derivative test.
Mathematics Archives
Math Archives: Visual Calculus: Drill First Derivative Test
A good worksheet for students to practice their first derivative skills. Allows you to check your answers by clicking the "solution" box.
Stefan Warner and Steven R. Costenoble
Finite Mathematics & Applied Calculus: Analyzing Graphs
Students learn about the features of a graph. Topics include intercepts, extrema, points of inflection, and end behavior. The tutorial explores the calculus concepts through notes and examples. Review exercises and a topic summary are...
Paul Dawkins
Paul's Online Notes: Calculus I: Applications of Derivatives
Learners examine applications of derivatives. Topics investigated are rates of change, the mean value theorem, optimization problems, critical points, linear approximations, and Newton?s method. Class notes, definitions, and examples...
Nine Planets
The Nine Planets: An Overview of the Solar System
A detailed overview of the history, mythology, and current scientific knowledge of each of the planets and moons in the solar system.
CK-12 Foundation
Ck 12: Factor Quadratics: Methods for Solving Quadratic Functions
[Free Registration/Login may be required to access all resource tools.] A review of the three major methods of solving quadratic functions for "x" intercepts.
Interactive Mathematics
Interactive Mathematics: Curve Sketching
Sketches of functions are drawn by determing important points: x- and y-intercepts, local maxima and minima, and point of inflection. The general shapes of specific functions are illustrated to help identify characteristics of each type...