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Ch 9: The Derivative at a Point

About This Chapter

Learn how to calculate a derivative of a function a particular point through a series of video lessons. The lessons all feature a self-assessment quiz to help you practice your skills and master the material.

The Derivative at a Point - Chapter Summary and Learning Objectives

The generic mathematical expression for a derivative comes from calculating the rate of change of a function. The rate of change allows you to understand a function's behavior around a particular input. This chapter explores how the derivative formula is related to the slope of a function's tangent line. The lessons allow you to form an intuitive understanding of derivatives and functions. Each lesson is taught by subject experts and features a transcript you can use to reference key terms. By the end of the chapter you will have understood:

  • How derivative functions represent real life phenomena such as velocity
  • How to create a line tangent to a function
  • Methods for writing the equation of the tangent line
  • How to discover the slopes of tangent lines
  • Steps to calculate a function's derivative

Video Objective
Velocity and the Rate of Change Examine the relationship of velocity with acceleration and time. Model velocity as a function of both.
Slopes and Rate of Change Discover how the slope of a tangent line can reveal a function's rate of change.
Equation of a Line Using Point-Slope Formula Learn how the point-slope formula can reveal a line's equation.
Interpreting the Slope & Intercept of a Linear Model Intuitively discover the constant nature of a linear function's slope and y-intercept.
Slopes and Tangents on a Graph Examine graphical representations of slopes and tangents.
Non Differentiable Graphs of Derivatives Learn the graphical characteristics of non differentiable functions and non differentiable derivatives.
First Derivative: Function, Examples & Quiz Explore the formal definition of a derivative and practically use it to discover the derivative of a function.
Finding Instantaneous Rate of Change of a Function: Formula & Examples Continue to apply the definition of a derivative to find the rate of change of various functions.
Calculating & Interpreting a Function's Average Rate of Change Discover the relationship between derivatives and the average rate of change, and how to calculate the latter.

9 Lessons in Chapter 9: The Derivative at a Point
Test your knowledge with a 30-question chapter practice test
Velocity and the Rate of Change

1. Velocity and the Rate of Change

Running from your little sister or just window-shopping, your speed is just a measure of how fast you move, or how your position is changing over time. In this lesson, learn about how velocity is a rate of change.

Slopes and Rate of Change

2. Slopes and Rate of Change

If you throw a ball straight up, there will be a point when it stops moving for an instant before coming back down. Consider this as we study the rate of change of human cannonballs in this lesson.

Equation of a Line Using Point-Slope Formula

3. Equation of a Line Using Point-Slope Formula

It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.

Interpreting the Slope & Intercept of a Linear Model

4. Interpreting the Slope & Intercept of a Linear Model

You've probably seen slope and intercept in algebra. These concepts can also be used to predict and understand information in statistics. Take a look at this lesson!

Slopes and Tangents on a Graph

5. Slopes and Tangents on a Graph

Hit the slopes and learn how the steepness of a line is calculated. Calculate the slopes between points and draw the tangents of curves on graphs in this lesson.

Non Differentiable Graphs of Derivatives

6. Non Differentiable Graphs of Derivatives

When I walk along a curve, I stand normal to it. That is, I stand perpendicular to the tangent. Learn how to calculate where I'm standing in this lesson.

First Derivative: Function & Examples

7. First Derivative: Function & Examples

In this lesson, you will learn about the relationship between the first derivative and rates of change. You will learn how to find the derivative of a polynomial using limits.

Calculating & Interpreting a Function's Average Rate of Change

8. Calculating & Interpreting a Function's Average Rate of Change

Average rates of change have many real-world applications. In this lesson, we'll learn how to calculate and interpret a function's average rate of change with easy-to-follow examples.

Finding Instantaneous Rate of Change of a Function: Formula & Examples

9. Finding Instantaneous Rate of Change of a Function: Formula & Examples

In this lesson, you will learn about the instantaneous rate of change of a function, or derivative, and how to find one using the concept of limits from Calculus.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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