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Instructional Video9:37
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\n\"Maxima\n\n
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\nCurated OER\n
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\nMaxima Minima Slope Intuition\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nBefore solving any problems, Sal gives an overview of what happens to the slope, first derivative, and second derivative at local maxima and minima to give the viewer a more intuitive feel for these types of problems.\n
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Worksheet
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\n\"Minima/Maxima\n\n
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\nCurated OER\n
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\nMinima/Maxima\n

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\n\nFor Students\n\n10th - 12th\n
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\nFor this minima/maxima worksheet, students solve systems of equations, identify the first derivative of a quadratic equation, and find the critical point in an equation. Using Excel worksheets, students graph four equations. There are...\n
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Worksheet
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\n\"Applications\n\n
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\nCurated OER\n
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\nApplications of Derivatives: Finding Maxima and Minima\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nIn this calculus worksheet, students are given 10 short-answer problems regarding functions, derivatives, minima, maxima and extremes.\n
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Instructional Video13:19
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\n\"Maxima\n\n
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\nKrista King Math\n
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\nMaxima and Minima On a Closed Interval\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nClose the chapter on extrema on a closed interval. Watching an informative video provides scholars with an opportunity to learn about extrema. Specifically, they see how to find the global maxima and minima on a closed interval by first...\n
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Worksheet
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\n\"Taylor\n\n
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\nCurated OER\n
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\nTaylor Polynomials, Minima, Maxima and Inflection Points\n

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\n\nFor Students\n\n12th - Higher Ed\n
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\nIn this Taylor polynomial worksheet, students answer 3 problems regarding quadratic polynomials, 2nd degree Taylor polynomials, and cubic polynomials.\n
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Worksheet
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\n\"Applications\n\n
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\nCurated OER\n
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\nApplications of Derivatives: Finding Maxima and Minima\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this derivative worksheet, 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 worksheet contains...\n
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Lesson Plan
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\n\"Maxima\n\n
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\nCurated OER\n
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\nMaxima and Minima Problems\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nStudents 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. \n
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Worksheet
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\n\"Maxima\n\n
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\nCurated OER\n
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\nMaxima and Minima\n

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\n\nFor Students\n\n9th - 11th\n
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\nIn this algebra worksheet, students discuss the origin of maxima and minima. They solve problems using the maxima and minima and graph parabolas and other functions containing a maxima and minima.\n
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\n\"Maxima\n\n
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\nCurated OER\n
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\nMaxima Minima Problems\n

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\n\nFor Students\n\n9th - 11th\n
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\nIn this algebra worksheet, students find the maxima and the minima of the parabola. They calculate the maximum and minimum area and apply the formulas of polygons to help them solve equations. There are 8 questions with an answer key.\n
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Interactive
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\n\"Derivatives\n\n
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\nCK-12 Foundation\n
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\nDerivatives with Mean Value Theorem and Rolle's Theorem: Maxima and Minima\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nRolle with the mean values and derivatives. Scholars complete the statements of Rolle's Theorem and the Mean Value Theorem. Using the interactive to illustrate scenarios, pupils respond to questions concerning the theorems in terms of...\n
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Worksheet
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\n\"Applications\n\n
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\nCurated OER\n
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\nApplications of Derivatives: General Rules for Optimization\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this minima and maxima activity, 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.\n
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Worksheet
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\n\"Basic\n\n
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\nCurated OER\n
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\nBasic Calculus: Extrema, and Optimization: Putting it all Together\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn 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...\n
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Organizer
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\n\"Applications\n\n
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\nCurated OER\n
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\nApplications of Derivatives: Finding Maxima and Minima\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this derivatives worksheet, students complete a function chart by telling the type of function, the derivative, and making an illustration of the concept. They find the intervals at which a given function is increasing or decreasing....\n
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Unit Plan
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\n\"Quadratic\n\n
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\nMathematics Vision Project\n
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\nQuadratic Functions\n

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\n\nFor Teachers\n\n10th - 12th\n\nStandards\n
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\nInquiry-based learning and investigations form the basis of a deep understanding of quadratic functions in a very thorough unit plan.  Learners develop recursive and closed methods for representing real-life situations,...\n
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Instructional Video9:18
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\n\"Optimization\n\n
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\nKrista King Math\n
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\nOptimization - Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nGet the maximum possible benefit from an optimal video. Scholars first review how to find critical points and how to test for local and global maxima and minima. They then apply these skills to a geometric optimization problem. \n
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Unit Plan
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\n\"Polynomial,\n\n
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\nPolynomial, Rational, and Radical Relationships\n

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\n\nFor Teachers\n\n9th - 12th\n\nStandards\n
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\nThis assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...\n
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Instructional Video9:44
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\n\"Graphing\n\n
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\nCurated OER\n
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\nGraphing with Calculus\n

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\n\nFor Students\n\n11th - Higher Ed\n
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\nIn a problem where you are not given the original function, but rather only three known points on the graph and a few additional pieces of information about when the first and second derivatives are positive or negative, Sal shows how...\n
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Lesson Plan
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\n\"Extreme\n\n
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\nCurated OER\n
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\nExtreme Values\n

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\n\nFor Teachers\n\n11th - Higher Ed\n
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\nLearners sketch a picture of what appears on a computer screen. Locate the extreme points on the pictures and label them as maxima or minima. Use the definitions of maxima and minima to explain how you identified the points indicated, if...\n
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Lesson Plan
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\n\"Worksheet\n\n
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\nCurated OER\n
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\nWorksheet 19 - Topographical Maps\n

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\n\nFor Teachers\n\nHigher Ed\n
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\nFor this map worksheet, pupils use information from given topical maps and locate the maxima and solve one dimensional wave equations. This two-page worksheet contains four problems.\n
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Lesson Plan
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\n\"The\n\n
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\nCurated OER\n
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\nThe Spider and the Fly\n

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\n\nFor Teachers\n\n11th - 12th\n
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\nStudents investigate maxima and minima by finding the shortest distance. In this calculus lesson, students calculate the shortest distance a bug travels to get to the other side of the tv. They analyze their findings discussing...\n
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Lesson Plan
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\n\"Quadratic\n\n
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\nCurated OER\n
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\nQuadratic Functions - Max and Min\n

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\n\nFor Teachers\n\n9th - 11th\n
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\nStudents identify the maxima and minima of quadratic functions. After a teacher explanation and demonstration of quadratic functions, students solve quadratic equations and graph the solution to find the maxima and minima of each...\n
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\n\"Absolute\n\n
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\nCurated OER\n
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\nAbsolute Maximum and Minimum\n

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\n\nFor Teachers\n\n9th - 11th\n
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\nLearners calculate the maximum and minimum of each function. In this algebra lesson, students collect and graph data to analyze it. They differentiate between the absolute max and min and the maxima and minima of each function.\n
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Worksheet
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\n\"Applications\n\n
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\nCurated OER\n
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\nApplications of Derivatives: Concavity and Optimization\n

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\nIn 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...\n
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Worksheet
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\n\"Finding\n\n
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\nCurated OER\n
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\nFinding Roots and Newton's Method\n

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\n\nFor Students\n\nHigher Ed\n
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\nIn this roots worksheet, students identify the local maxima and minima for a function. Students find the roots of the function using roots and Newton's Method of approximation. This three-page worksheet contains examples, explanations...\n
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