Defining Average and Instantaneous Rates of Change at a Point

Defining the Derivative of a Function and Using Derivative Notation

Estimating Derivatives of a Function at a Point

Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist

Applying the Power Rule

The Chain Rule

Implicit Differentiation

Differentiating Inverse Functions

Differentiating Inverse Trigonometric Functions

Selecting Procedures for Calculating Derivatives

Interpreting the Meaning of the Derivative in Context

Straight-Line Motion: Connecting Position, Velocity, and Acceleration

Rates of Change in Applied Contexts other than Motion

Intro to Related Rates

Solving Related Rates Problems

Using the Mean Value Theorem

Extreme Value Theorem, Global vs Local Extrema, and Critical Points

Determining Intervals on Which a Function is Increasing or Decreasing

Using the First Derivative Test to Determine Relative (Local) Extrema

Using the Candidates Test to Determine Absolute (Global) Extrema

Integration and Accumulation of Change

Approximating Areas with Riemann Sums

Riemann Sums, Summation Notation, and Definite Integral Notation

The Fundamental Theorem of Calculus and Accumulation Functions

Interpreting the Behavior of Accumulation Functions Involving Area

Modeling Situations with Differential Equations

Verifying Solutions for Differential Equations

Sketching Slope Fields

Reasoning Using Slope Fields

Approximating Solutions Using Euler’s Method

Finding the Average Value of a Function on an Interval

Connecting Position, Velocity, and Acceleration of Functions Using Integrals

Using Accumulation Functions and Definite Integrals in Applied Contexts

Finding the Area Between Curves Expressed as Functions of x

Finding the Area Between Curves Expressed as Functions of y

Defining and Differentiating Parametric Equations

Second Derivatives of Parametric Equations

Finding Arc Lengths of Curves Given by Parametric Equations

Defining and Differentiating Vector-Valued Functions

Integrating Vector-Valued Functions

Defining Convergent and Divergent Infinite Series

Working with Geometric Series

The nth Term Test for Divergence

Integral Test for Convergence

Harmonic Series and p-Series