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81 lessons across 8 topics
Connecting a Function Its First Derivative, and Its Second Derivative
Determining Concavity of Functions over Their Domains
Determining Intervals on Which a Function is Increasing or Decreasing
Exploring Behaviors of Implicit Relations
Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
Introduction to Optimization Problems
Sketching Graphs of Functions and their Derivatives
Solving Optimization Problems
Using the Candidates Test to Determine Absolute (Global) Extrema
Using the First Derivative Test to Determine Relative (Local) Extrema
Using the Mean Value Theorem
Using the Second Derivative Test to Determine Extrema
Connecting Position, Velocity, and Acceleration of Functions Using Integrals
Finding the Area Between Curves Expressed as Functions of x
Finding the Area Between Curves Expressed as Functions of y
Finding the Area Between Curves That Intersect at More Than Two Points
Finding the Average Value of a Function on an Interval
Using Accumulation Functions and Definite Intervals In Applied Contexts
Volume with Disc Method: Revolving Around Other Axes
Volume with Disc Method: Revolving Around the x- or y-Axis
Volume with Washer Method: Revolving Around Other Axes
Volume with Washer Method: Revolving Around the x- or y-Axis
Volumes with Cross Sections: Squares and Rectangles
Volumes with Cross Sections: Triangles and Semicircles
Approximating Values of a Function Using Local Linearity and Linearization
Interpreting the Meaning of the Derivative in Context
Introduction to Related Rates
Rates of Change in Applied Concepts Other Than Motion
Solving Related Rates Problems
Straight-Line Motion: Connecting Position, Velocity, and Acceleration
Using L'Hospital's Rule for Determining Limits of Indeterminate Forms
Exponential Models with Differential Equations
Finding General Solutions Using Separation of Variables
Finding Particular Solutions Using Initial Conditions and Separation of Variables
Modeling Situations with Differential Equations
Reasoning Using Slope Fields
Sketching Slope Fields
Verifying Solutions for Differential Equations
Applying the Power Rule
Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist
Defining Average and Instantaneous Rate of Change at a Point
Defining the Derivative of a Function Using Derivative Notation
Derivative Rules: Constant, Sum, Difference, and Constant Multiple
Derivatives of cos x, sin x, ex, and ln x
Estimating Derivatives of a Function at a Point
Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions
The Product Rule
The Quotient Rule
Applying Properties of Definite Integrals
Approximating Areas With Riemann Sums
Exploring Accumulations of Change
Finding Antiderivatives and Indefinite Integrals: Basc Rules and Notation
Integrating Functions Using Long Division and Completing the Square
Integrating Using Substitution
Interpreting the Behavior of Accumulation Functions Involving Area
Riemann Sums, Summation Notation, and Definite Integral Notation
Selecting Techniques for Antidifferentiation
The Fundamental Theorem of Calculus and Accumulation Functions
The Fundamental Theorem of Calculus and Definite Intervals
Confirming Continuity over an Interval
Connecting Infinite Limits and Vertical Asymptotes
Connecting Limits at Infinity and Horizontal Asymptotes
Connecting Multiple Representations of Limits
Defining Continuity at a Point
Defining Limits and Using Limit Notation
Determining Limits Using Algebraic Manipulation
Determining Limits Using Algebraic Properties of Limits
Determining Limits Using the Squeeze Theorem
Estimating Limit Values from Graphs
Estimating Limit Values from Tables
Exploring Types of Discontinuities
Introducing Calculus: Can Change Occur at an Instant?
Removing Discontinuities
Selecting Procedures for Determining Limits
Working With the Intermediate Value Theorem (IVT)