Important Terms and Concepts

Learning OutcomesIn this chapter, students will...

Chapter 3 Sections
31 Graphical Interpretation of Derivative
Objective: Given the equation of a function, calculate the derivative at a given point by taking the limit of the quantity (change in y)/(change in x)
Homework: Problems 18 all
Objective: Given the equation of a function, calculate the derivative at a given point by taking the limit of the quantity (change in y)/(change in x)
Homework: Problems 18 all
32 Difference Quotients and One Definition of Derivative
Objective: Given the equation of a function, and a value of x, use the definition of derivative to calculate algebraically the value of the derivative at that point, and confirm your answer numerically and graphically.
Homework: Q Problems 110, 1, 2, 311 odd
Objective: Given the equation of a function, and a value of x, use the definition of derivative to calculate algebraically the value of the derivative at that point, and confirm your answer numerically and graphically.
Homework: Q Problems 110, 1, 2, 311 odd
33 Derivative Functions, Numerically and Graphically
Objective: Given the equation of a function, graph the function and its (numerical) derivative function on the same set of axes, and make conjectures about the relationship between the derivative function and the original function.
Aligned Instructional Resources: Interactive Flash "Derivative Grapher" Demonstration
Homework: Q Problems 110, 113 odd, 1417 all
Objective: Given the equation of a function, graph the function and its (numerical) derivative function on the same set of axes, and make conjectures about the relationship between the derivative function and the original function.
Aligned Instructional Resources: Interactive Flash "Derivative Grapher" Demonstration
Homework: Q Problems 110, 113 odd, 1417 all
34 Derivative of the Power Function and Another Definition of Derivative
Objective: Given a power function, ƒ(x)=x^n, where n stands for a constant, or given a linear combination of power functions, find an equation expressing ƒ'(x) in terms of x.
Homework  Day 1: Q Problems 110, 118 all, 1923 odd
Homework  Day 2: 25, 26, 2932 all
Objective: Given a power function, ƒ(x)=x^n, where n stands for a constant, or given a linear combination of power functions, find an equation expressing ƒ'(x) in terms of x.
Homework  Day 1: Q Problems 110, 118 all, 1923 odd
Homework  Day 2: 25, 26, 2932 all
35 Displacement, Velocity, and Acceleration
Objective: Given an equation for the displacement of a moving object, find an equation for its velocity and an equation for its acceleration, and use the equations to analyze the motion.
Homework  Day 1: Q Problems 110, 1, 2, 5, 6 and 7
Homework  Day 2: 9, 11, 12, 1518 all, 21, 22
Objective: Given an equation for the displacement of a moving object, find an equation for its velocity and an equation for its acceleration, and use the equations to analyze the motion.
Homework  Day 1: Q Problems 110, 1, 2, 5, 6 and 7
Homework  Day 2: 9, 11, 12, 1518 all, 21, 22
36 Introduction to Sine, Cosine, and Composite Functions
Objective: Work with your study group to form conjectures on how to differentiate a composite function.
Homework: Problems 17 in class
Objective: Work with your study group to form conjectures on how to differentiate a composite function.
Homework: Problems 17 in class
37 Derivatives if Composite Functions  The Chain Rule
Objective: Given the equation for a composite function, write the equation for its derivative function.
Homework  Day 1: Q Problems 110, 110 all
Homework  Day 2: Problems 1120 all
Homework  Day 3: Problems 2130 all
Objective: Given the equation for a composite function, write the equation for its derivative function.
Homework  Day 1: Q Problems 110, 110 all
Homework  Day 2: Problems 1120 all
Homework  Day 3: Problems 2130 all
38 Proof and Application of Sine and Cosine Derivatives
Objective: Be able to derive algebraically the formulas for the derivatives of sin x and cos x. Find rates of change of sinusoidal functions in realworld problems.
Homework  Day 1: Q Problems 110, 1, 3, 7
Homework  Day 2: Problems 8, 13, 14
Objective: Be able to derive algebraically the formulas for the derivatives of sin x and cos x. Find rates of change of sinusoidal functions in realworld problems.
Homework  Day 1: Q Problems 110, 1, 3, 7
Homework  Day 2: Problems 8, 13, 14
39 Exponential and Logarithmic Functions
Objective: Given an exponential or logarithmic function, find its derivative function algebraically.
Homework  Day 1: Q Problems 110, 1, 3, 510 all
Homework  Day 2: Problems 2, 4, 1116 all
Homework  Day 3: Problems 1730 all
Objective: Given an exponential or logarithmic function, find its derivative function algebraically.
Homework  Day 1: Q Problems 110, 1, 3, 510 all
Homework  Day 2: Problems 2, 4, 1116 all
Homework  Day 3: Problems 1730 all