Definition of the Derivative Part 2
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Lesson Description:
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.
Check out www.themathdude.org for more videos.
Additional Resources:
- 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
- Notes - Coaxing the Derivative out of NOTHING Notes
Questions answered by this video:
- 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?
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Staff Review
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.
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