CK-12 Foundation
Absolute Extrema and Optimization: Building the Biggest Box
Optimally, you want the largest box. Given a square piece of box material, pupils determine the size of congruent squares to cut out of the corners to create a box with the greatest volume. Learners determine the equation of the volume...
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Calculus AB/BC - Introduction to Optimization Problems
Let's get the equation set. Pupils see the importance of setting up an one-variable equation in the first of two lessons on optimization problems. The presenter works four different types of problems before individuals use the included...
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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...
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Calculus AB/BC - Solving Optimization Problems
Move beyond setting up equations. Pupils continue with optimization problems and use their knowledge of derivatives to find solutions. They watch as the video uses equations from previous examples and find solutions to answer specific...
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Optimization
Learners identify the critical points to a function. In this calculus lesson, students perform optimization of functions. They use the TI to create a visual of the graph.
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Application of Differentiation: Optimization
In this optimization worksheet, students complete a table identifying the characteristics of a function and it's derivative and provide an illustration of each type of function. Afterward, they use the first derivative test for finding...
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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...
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Applications of Derivatives: Optimization
In this optimization worksheet, students write a short essay listing the criterion for global minimum. They write directions for finding the global minimum on a closed or open interval.
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Applications of Derivatives: Finding Maxima and Minima
In this derivative 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 activity contains...
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Maximum/ Minimum Problems
For this optimization worksheet, students solve 20 short answer word problems. Students read, sketch, define variables, write equations, differentiate their equations, and find the maximum or minimum of each word problem.
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Basic Calculus: Extrema, and Optimization: Putting it all Together
In this extrema and optimization activity, 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 activity contains two...
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Multivariable Optimization
In this multivariable optimization instructional activity, students determine the local maximum and local minimum of given functions. They identify the critical points for given function and match contour plots to the proper functions....
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Applications of Derivatives: General Rules for Optimization
In this minima and maxima worksheet, students find the global and local maxima and minima of one function. They work in small groups to solve one optimization problem. Steps for solving are listed on the page.
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Extrema on an Interval
Learners explore maximum and minimum points, slopes and tangents. In this Pre-Calculus lesson, students solve optimization problems and find rates of change.
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Healthy Computer Ergonomics
Middle schoolers identify, demonstrate properly, and apply correct position and posture while working at the computer. They also demonstrate optimal posture and position at the computer workstation, including: sitting up with the arms...
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Finding Extrema Graphically and Symbolically
In this extrema instructional activity, 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...
Radford University
Throwing a Football
Use mathematics to help the football team. Pairs brainstorm how to approach finding a solution to a problem to help the quarterback complete more passes. By researching and collecting data, the teams derive an equation to represent the...
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Implicit Differentiation
In this implicit differentiation worksheet, students use the microscope approximation method and Euler's method to approximate values at a given point. This two-page worksheet contains five problems.
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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...
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Maxima and Minima Problems
Students calculate the maxima and minima of quadratic equations. In this calculus lesson, students apply the derivatives by finding the maxima and minima using real life application. They solve optimization using the derivative.
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The Apple Orchard Problem
Students explore various approaches to solving a problem of maximizing the total production of apples in an orchard. For this apple orchard lesson, students collect data in order to solve the apple orchard problem presented. Students...
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The Corner Problem
Students explore the concept of the corner problem. In this corner problem lesson, students use the TI-NSpire to determine the maximum length a rod can be and still pass horizontally around a corner. Students use similar triangles to...
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Engineering in a Calculus Classroom
Students solve several differential equations. In this calculus lesson, students test their modulus calculation by testing different weights or beam lengths. They share their findings in class.
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Functions of Two Variables
In this function of two variables worksheet, students explore the relationship between the derivatives of a function and the shape of the graph. They determine the maximum and minimum value using optimization. Students find the...