MR. BISHOP'S MATH RESOURCES
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  • Integrated Math 3
    • Homework Calendars
    • Chapter 2 - Linear Equations, Inequalities, and Functions >
      • 2-1/2-2 Solving Equations/Inequalities
      • 2-3 Linear Functions and Slope-Intercept Form
      • 2-4 Families of Functions
      • 2-5 Absolute Value Functions and Graphs
      • 2-6 Two-Variable Inequalities
      • 2-7 Solving Systems of Equations
      • 2-8 Systems of Inequalities
      • 2-9 Systems With Three Variables
      • Chapter 2 Reviews
    • Chapter 3 - Quadratic Functions and Equations >
      • 3-1 Quadratic Functions and Transformations
      • 3-2 Standard Form of a Quadratic Function
      • 3-3 Factoring Quadratic Expressions
      • 3-3b Intercept Form
      • 3-4 Quadratic Equations
      • Graphing Quadratics Handouts
      • 3-5 Completing the Square
      • 3-6 The Quadratic Formula
      • Chapter 3 Reviews
    • Chapter 4 Polynomials and Polynomial Functions >
      • 4-1 Polynomial Functions
      • 4-2 Adding, Subtracting, and Multiplying Polynomials
      • 4-3 Polynomials, Linear Factors, and Zeros
      • 4-4 Solving Polynomial Equations
      • 4-5 Dividing Polynomials
      • 4-6 Theorems About Roots of Polynomial Equations
      • Chapter 4 Handouts
      • Chapter 4 Reviews
    • Chapter 5 - Rational Expressions and Functions >
      • 5-1 Simplifying Rational Expressions
      • 5-2 Multiplying and Dividing Rational Expressions
      • 5-3 Adding and Subtracting Rational Expressions
      • 5-5 The Reciprocal Function Family
      • 5-7 Solving Rational Equations
      • Chapter 5 Handouts
      • Chapter 5 Reviews
    • Chapter 6 - Radical Expressions and Functions >
      • 6-1 Roots and Radical Expressions
      • 6-2 Multiplying and Dividing Radical Expressions
      • 6-3 Binomial Radical Expressions
      • 6-4 Rational Exponents
      • 6-5 Solving Square Root and Other Radical Equations
      • 6-6 Functions Operations
      • 6-7 Inverse Relations and Functions
      • 6-8 Graphing Radical Functions
      • Chapter 6 Handouts
      • Chapter 6 Reviews
    • Chapter 7 - Exponential and Logarithmic Functions >
      • 7-1 Exploring Exponential Models
      • 7-2 Properties of Exponential Functions
      • 7-3 Logarithmic Functions as Inverses
      • 7-4 Properties of Logarithms
      • 7-5 Exponential and Logarithmic Equations
      • 7-6 Natural Logarithms
      • Chapter 7 Handouts
      • Chapter 7 Reviews
    • Chapter 8 - Trigonometric Functions >
      • 8-0 Right Triangle Trigonometry
      • 8-1 Exploring Periodic Data
      • 8-2 Angles and the Unit Circle
      • 8-3 Radian Measure
      • Chapter 8 Handouts
      • Chapter 8 Reviews
    • Spring 2019 Final Project
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Chapter 3 - Derivatives

3.1 Derivative of a Function
3.2 Differentiability
3.3 Rules for Differentiation
3.4 Velocity and Other Rates of Change
3.5 Derivatives of Trigonometric Functions
Chapter 3 Reviews

In Chapter 2, we learned how to find the slope of a tangent to a curve as the limit of the slopes of secant lines.  In section 2.4, a formula was derived for the slope of the tangent at an arbitrary point (a, 1/a) on the graph of the function f(x) = 1/x and showed it was -1/a^2.
This result is more powerful than it might appear at first glance, as it gives us a simple way to calculate the instantaneous rate of change of f at any point.  The study of rates of change of functions is called differential calculus, and the formula -1/a^2 was our first look at a derivative.  The derivative was the 17th-century breakthrough that enabled mathematicians to unlock the secrets of planetary motion and gravitational attraction -- of objects changing position over time.  We will learn many uses for derivatives in Chapter 5, but first, in the next two chapters, we will focus on what derivatives are and how they work.
​ (Taken from an excerpt in the fifth edition of the Finney, Demana, Waits, Kennedy, and Bressoud textbook Calculus - Graphical, Numerical, Algebraic.)


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  • Home
  • Integrated Math 3
    • Homework Calendars
    • Chapter 2 - Linear Equations, Inequalities, and Functions >
      • 2-1/2-2 Solving Equations/Inequalities
      • 2-3 Linear Functions and Slope-Intercept Form
      • 2-4 Families of Functions
      • 2-5 Absolute Value Functions and Graphs
      • 2-6 Two-Variable Inequalities
      • 2-7 Solving Systems of Equations
      • 2-8 Systems of Inequalities
      • 2-9 Systems With Three Variables
      • Chapter 2 Reviews
    • Chapter 3 - Quadratic Functions and Equations >
      • 3-1 Quadratic Functions and Transformations
      • 3-2 Standard Form of a Quadratic Function
      • 3-3 Factoring Quadratic Expressions
      • 3-3b Intercept Form
      • 3-4 Quadratic Equations
      • Graphing Quadratics Handouts
      • 3-5 Completing the Square
      • 3-6 The Quadratic Formula
      • Chapter 3 Reviews
    • Chapter 4 Polynomials and Polynomial Functions >
      • 4-1 Polynomial Functions
      • 4-2 Adding, Subtracting, and Multiplying Polynomials
      • 4-3 Polynomials, Linear Factors, and Zeros
      • 4-4 Solving Polynomial Equations
      • 4-5 Dividing Polynomials
      • 4-6 Theorems About Roots of Polynomial Equations
      • Chapter 4 Handouts
      • Chapter 4 Reviews
    • Chapter 5 - Rational Expressions and Functions >
      • 5-1 Simplifying Rational Expressions
      • 5-2 Multiplying and Dividing Rational Expressions
      • 5-3 Adding and Subtracting Rational Expressions
      • 5-5 The Reciprocal Function Family
      • 5-7 Solving Rational Equations
      • Chapter 5 Handouts
      • Chapter 5 Reviews
    • Chapter 6 - Radical Expressions and Functions >
      • 6-1 Roots and Radical Expressions
      • 6-2 Multiplying and Dividing Radical Expressions
      • 6-3 Binomial Radical Expressions
      • 6-4 Rational Exponents
      • 6-5 Solving Square Root and Other Radical Equations
      • 6-6 Functions Operations
      • 6-7 Inverse Relations and Functions
      • 6-8 Graphing Radical Functions
      • Chapter 6 Handouts
      • Chapter 6 Reviews
    • Chapter 7 - Exponential and Logarithmic Functions >
      • 7-1 Exploring Exponential Models
      • 7-2 Properties of Exponential Functions
      • 7-3 Logarithmic Functions as Inverses
      • 7-4 Properties of Logarithms
      • 7-5 Exponential and Logarithmic Equations
      • 7-6 Natural Logarithms
      • Chapter 7 Handouts
      • Chapter 7 Reviews
    • Chapter 8 - Trigonometric Functions >
      • 8-0 Right Triangle Trigonometry
      • 8-1 Exploring Periodic Data
      • 8-2 Angles and the Unit Circle
      • 8-3 Radian Measure
      • Chapter 8 Handouts
      • Chapter 8 Reviews
    • Spring 2019 Final Project
  • About
  • Contact