Published at : 10 Sep 2021

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What is a derivative? Learn what a derivative is, how to find the derivative using the difference quotient, and how to use the derivative to find the equation of the tangent line. This is a free math video tutorial by Marioβs Math Tutoring.

0:11 What is a Derivative

1:22 Finding the Slope Between 2 Points on a Curve

2:05 Difference Between the Average Rate of Change and the Instantaneous Rate of Change

2:34 Using Limits to Find the Instantaneous Rate of Change

3:15 What is the Difference Quotient

3:23 Notation for the Derivative

3:46 Example 1 Finding the Derivative of f(x)=x^2 Using Difference Quotient

5:02 Using the Derivative to Find the Slope at a Point

5:26 Writing the Equation of the Tangent Line at a Point

6:00 Example 2 f(x)=x^3 - 4x Finding the Derivative to Find the Relative Maximum and Minimums

7:40 Using the Difference Quotient to find the Derivative

7:57 Using the Binomial Expansion Theorem to Simplify

8:54 Setting the Derivative to Zero to Find Turning Points

9:35 Graphing the Polynomial With the Turning Points

10:07 Summary of What the Deriviative is, How to Find it, and How to Use It

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