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Math 155 - Worksheet 13. Intervals
In this interval learning exercise, 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...
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Worksheet 22-Fall 1995
In this math learning exercise, students examine the graph of the derivative. Then they determine the critical points that correspond to the relative extrema.
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Applications of Derivatives: Newton's Method
In this derivative worksheet, students use Newton's Method for finding the roots of a function. They identify the local extrema and discuss ways in which Newton's Method can fail. This one-page worksheet contains four problems.
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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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Lesson #67 Relative Extrema
Students test for relative extrema. In this Calculus lesson, 12th graders investigate the relative extrema of a function and sketch the curve from the given information without the use of a calculator.
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Fundamental Theorem of Calculus
High schoolers, with the assistance of their TI-84 Plus / TI-83 Plus calculators, explore and assess the connections between an accumulation function, one defined by a definite integral, and the integrand. They summarize that the...
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Extrema on an Interval
Students explore maximum and minimum points, slopes and tangents. For this Pre-Calculus lesson, students solve optimization problems and find rates of change.
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Analyze This Function
In this derivatives activity, students solve 11 short answer and graphing problems. Students find inflection points, increasing and decreasing intervals, maximums and minimums, and graph an exponential derivative. Students use the...
Flipped Math
Calculus AB/BC Mid-Unit 5 Review: Analytical Applications of Differentiation
It's time to put analytical applications to work. Learners use the eight questions of the mid-Unit 5 review to refresh their memories of the key points. Pupils apply what they have learned to use the Mean Value Theorem, find extrema...
CCSS Math Activities
Smarter Balanced Sample Items: High School Math – Target E
Pupils rewrite expressions in equivalent forms to identify key features. They use the vertex and factored forms of quadratic expressions to identify the extrema and intercepts. To finish the installment of the Claim 1 Item Slide Show...
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Math Handbook: Calculus
If only there was a reference that listed all the formulas covered in calculus. Luckily, there is. This comprehensive 197-page handbook provides formulas and explanations for all topics in AP Calculus or in a standard college calculus...
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Graphing Factored Polynomials
Young mathematicians graph polynomials using the factored form. As they apply all positive leading coefficients, pupils demonstrate the relationship between the factors and the zeros of the graph.
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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...
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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. In this apple orchard lesson, students collect data in order to solve the apple orchard problem presented. Students plot...
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River Optimization Problem
Learners 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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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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More on Limits, Graph Sketching, and L'Hopital's Rule
For this limits worksheet, students compute the answers to thirteen limits problems. They answer one short answer question. Students follow listed steps to simplify two limits problems. Students answer three short answer questions about...
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Challenge Discussion Sheet 6
Students are challenged to determine values that are guaranteed by the mean value theorem. They sketch the graph of a function and show that it satisfies the conditions of the mean value theorem over a given interval. Students determine...
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Critical Points
Students identify critical points on a graph. In this calculus instructional activity, students graph their equations on the TI calculator. They zoom in and out to identify the critical points.
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Introduction to Tangent Lines using the TI-Nspire
Young scholars make mathematical argument using the concept of Limit. In this algebra lesson, student calculate the instantaneous rate of change from the linear graph. They use a TI-calculator to create a visual of the graphs.
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The First Fundamental Theorem of Calculus
Solve problems using the fundamental theorem. In this calculus lesson, students solve problems using theorems and proving theorems. They derive the fundamental theorem as they study it.
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Linear Approximation
In this algebra worksheet, students solve problems using estimation and the derivative. They calculate the critical points, domain and indicated intervals. They calculate the first and second derivative. There are 5 problems.
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Applications of First and Second Derivatives.
In this calculus worksheet, students solve for the critical values, open intervals and find the maximum and minimum. There are 7 questions dealing with the derivative.
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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.