12 videos in "Tangent Lines and Slope"

Rates of Change and Related Rates

Tangent Lines and Velocity

Derivatives and Tangent Lines 1

Derivatives and Tangent Lines 2

Derivatives and Tangent Lines 3

Derivatives and Tangent Lines 4

[C.1] AROC  Part 1  in a table

[C.1] AROC  Part 2  with difference quotient

Secant Line and AROC

Definition of the Derivative Part 1

Definition of the Derivative Part 2

IROC vs AROC
Definition of the Derivative Part 2
Definition of the Derivative Part 2
1500 views, 2 ratings  00:02:48
Part of video series Rate of Change of Relationships / Functions
Check out www.themathdude.org for more videos.
(
download video
)
Be able to explain the definition of the derivative (THE fundamental notion of Calculus) in terms of a limit of the difference quotient and more importantly the Cartesian plot of secant lines vs tangent line to a function.
 Notes  Coaxing the Derivative out of NOTHING Notes
 Leibniz's notation  Explanation and function notation of Leibniz's notation
 Leibniz notation Yahoo Answer  Can't understand Leibniz notation? Read this explanation of it on Yahoo Answers
 Java Applet  Secant to Tangent line  A Java applet that allows you to approximate a tangent line by using secant lines
 How can you use a secant line to approximate the slope of a curve at a point?
 How can you make two points on a secant line approach each other?
This lesson picks up where the previous video left off, moving the two points on the secant line closer and closer together. This is explained very well to make the claim that you need two points that approach each other so their distance approaches, but never reaches, 0.