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Home › Courses › Calculus 1/AB/BC › Archive for Chapter 3 – Uses of the Derivative
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Chapter 3 – Uses of the Derivative

This chapter is all about the awesome applications of derivatives!  You begin with absolute extrema and finding critical numbers.  Then it is off to Rolle’s and the Mean Value Theorems.  From there your quest takes you through using f ‘ to figure out where f is increasing and decreasing along with rocking the First Derivative Test!  The study of the second derivative, f “, and the concavity and points of inflection of f is the next important stop.  The 2nd derivative test is explored.  You will then learn how to sketch curves using all of the calculus rocked thus far.  You will master the fun and classic lesson on optimization and make easy work of tangent line approximations (local linearization) and differentials.  From there, you will make quick work of Newton’s method.  TONS of original AB and BC Exam practice problems all about the applications of the derivative close out the chapter!

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Lesson 1 – Absolute Maximum, Minimum, and Critical Numbers

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Lesson 1 – Absolute Maximum, Minimum, and Critical Numbers (Part 2)

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Lesson 2 – Rolle’s and Mean Value Theorems

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Lesson 2 – Rolle’s and Mean Value Theorems (Part 2)

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Lesson 3 – Increasing and Decreasing & The First Derivative Test

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Lesson 3 – Increasing and Decreasing & The First Derivative Test (Part 2)

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Lesson 4 – Concavity and Point of Inflection

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Lesson 4 – Concavity and Point of Inflection (Part 2)

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Lesson 5 – Curve Sketching

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Lesson 5 – Curve Sketching (Part 2)

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Lesson 6 – Optimization

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Lesson 6 – Optimization (Part 2)

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Lesson 7 – Tangent Line Approximation and Differentials

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Lesson 7 – Tangent Line Approximation and Differentials (Part 2)

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Lesson 8 – Newton’s Method

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Lesson 9 – Calculus AB and BC Exam Practice on Derivative Applications

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Lesson 9 – Calculus AB and BC Exam Practice on Derivative Applications (Part 2)

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Lesson 9 – Calculus AB and BC Exam Practice on Derivative Applications (Part 3)

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      • 6th Grade Math
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Whole Numbers & Decimals
        • Chapter 2: Representing Data In Different Ways
        • Chapter 3: Variables, Algebraic Expressions, & Solving Equations
        • Chapter 4: Divisibility, Factoring Numbers, & Fractions
        • Chapter 5: Addition and Subtraction of Fractions
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        • Chapter 7: Ratios, Proportions, and Percents
        • Chapter 8: Fundamentals of Geometry
        • Chapter 9: Unit Conversions, Perimeter, Area, & Volume
        • Chapter 10: Introduction to Probability
        • Chapter 11: Integers – Properties, Operations, & Equations
        • Chapter 12: Two-Step Equations and Inequalities
      • Pre-Algebra
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions & Operations with Integers
        • Chapter 2: One-Step Equations & Inequalities
        • Chapter 3: Operations and Equations With Decimals
        • Chapter 4: Factors, Simplifying Fractions, and Exponent Rules
        • Chapter 5: Fraction Operations & Solving Equations with Fractions
        • Chapter 6: Operations and Uses of Ratios, Proportions, & Percents
        • Chapter 7: Solving Equations and Inequalities
        • Chapter 8: Relations & Functions, Slope, Lines, and Graphing
        • Chapter 9: Foundations of Geometry
        • Chapter 10: Areas of Two- & Three-Dimensional Figures and Volume
        • Chapter 11: Right Triangles and An Introduction to Trigonometry
        • Chapter 12: Data Analysis: Techniques and Calculations
        • Chapter 13: Probability, Combinations, and Permutations
        • Chapter 14: Foundations of Non-Linear Functions and Polynomial Operations
      • Algebra 1
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions and Operations with Real Numbers
        • Chapter 2: Solving Equations – From One-Step to Multi-Step
        • Chapter 3: Ratios, Proportions, & Percents
        • Chapter 4: Solving Inequalities
        • Chapter 5: Introduction to Graphs and Functions
        • Chapter 6: Linear Functions and Graphing Lines
        • Chapter 7: Systems of Linear Equations and Linear Inequalities
        • Chapter 8: Exponent Rules & Exponential Functions
        • Chapter 9: Polynomials
        • Chapter 10: Graphing and Solving Quadratic Equations
        • Chapter 11: Introduction to Rational Expressions
        • Chapter 12: Radicals and An Introduction to Trigonometry
        • Chapter 13: Data Analysis: Techniques and Calculations
        • Chapter 14: Probability, Combinations, and Permutations
      • Calculus 1 & 2 / AB / BC
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1 – Limits
        • Chapter 2 – Derivatives
        • Chapter 3 – Uses of the Derivative
        • Chapter 4 – Integration
        • Chapter 5 – Derivatives and Integrals of Exponential Functions, Logarithms, and Inverse Trigonometry
        • Chapter 6 – Differential Equations and Exponential & Logistic Growth
        • Chapter 7 – Area, Volume, and Arc Length
        • Chapter 8 – Advanced Integration Techniques and Improper Integrals
        • Chapter 9 – Series and Tests for Convergence and Divergence
        • Chapter 10 – Taylor Polynomials and Power Series
        • Chapter 11 – The Calculus of Parametric and Polar Equations
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