MA005: Derivatives and Tangent Lines

Watch this video (until 8:12) on how to find the slopes of tangent lines from a graph.

Source: Linda Green, https://www.youtube.com/watch?v=zfCdXazyeGI
This work is licensed under a Creative Commons Attribution 3.0 License.

Last modified: Friday, June 21, 2024, 12:16 PM

Course Syllabus

Course Syllabus

Unit 1: Preview and Review

1.1: Preview of Calculus

Preview of Calculus

Derivatives and Tangent Lines

Find the Area of an Irregular Shape

Practice Problems

1.2: Lines in the Plane

Lines in the Plane

Find a Slope Given Two Points

Find the Equation of a Line Given Two Points

Equations of Circles: Radius and Center

How to Find the Equation of a Line from a Slope and Point

Determine the Equation of a Line Parallel to a Line in General Form

Determine the Equation of a Line Perpendicular to a Line in Slope-Intercept Form

Practice Problems

1.3: Functions and Their Graphs

Functions and Their Graphs

Evaluate Function at a Point

Practice Problems

1.4: Combinations of Functions

Combinations of Functions

More on the Composition of Functions

Combine Functions using Algebraic Operations

Practice Problems

1.5: Mathematical Language

Mathematical Language

Negating Quantified Statements

Converse and Contrapositive

Practice Problems

Unit 2: Functions, Graphs, Limits, and Continuity

2.1: Tangent Lines, Velocities, and Growth

Tangent Lines, Velocities, and Growth

Slope of a Function at a Point

Practice Problems

2.2: The Limit of a Function

The Limit of a Function

Evaluating Limits Using a Graph

More on the Limit of a Function

The Limit of Laws

Practice Problems

2.3: Properties of Limits

Properties of Limits

Solving Limits (Rationalization)

Calculating Slope of Tangent Line Using the Definition of a Derivative

Practice Problems

2.4: Continuous Functions

Continuous Functions

More on Continuous Functions

Intermediate Value Theorem

Practice Problems

2.5: Definition of a Limit

Definition of a Limit

Epsilon-Delta Limits

Practice Problems

Unit 2 Assessment

Unit 2 Assessment

Unit 3: Derivatives

3.1: Introduction to Derivatives

Introduction to Derivatives

The Tangent Line

Practice Problems

3.2: The Definition of a Derivative

The Definition of a Derivative

Derivatives from the Definition

Practice Problems

3.3: Derivatives, Properties, and Formulas

Derivatives, Properties, and Formulas

Applying the Product Rule for Derivatives

Practice Problems

3.4: Derivative Patterns

Derivative Patterns

The Power Rule for Polynomials

Derivatives of Exponential Functions

Derivatives of Trigonometric Functions

Higher-Ordered Derivatives

Practice Problems

3.5: The Chain Rule

The Chain Rule