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 1
Definition of the Derivative Part 1
3520 views, 2 ratings  00:07:12
Part of video series Rate of Change of Relationships / Functions
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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
 What is the formal definition of a derivative?
 What is the limit notation for a derivative?
 How do you approximate a derivative?
 How do you find the average rate of change or slope of the secant line between two points that are very close together on a curve?
 How do you find the slope of a function at a point?
 What happens as h gets smaller and smaller as you try to get two points on a secant line as close together as possible to find the slope at a point of a function?
This lesson shows the formal definition of a derivative using limit notation and explains the concept of the derivative. You will also see how to approximate the derivative of a function at a point. This lesson is a great introduction to derivatives. There is a glitch at the end of this video, so it continues into the next video.