Definition of the Derivative Part 1
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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.
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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:
- 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?
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Staff Review
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.
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