# Ch 9: The Derivative at a Point

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
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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