Derivatives and Tangent Lines 4
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Lesson Summary:
In this lesson, we learn about the formula for the derivative and how it gives us the slope of a tangent line to a curve. We see how to find the derivative for a linear function and how the slope of the tangent line is the same as the slope of the line itself. We also practice finding the derivative for a quadratic function and seeing how the slope of the tangent line varies at different points on the curve.
Lesson Description:
An introduction to derivatives and tangent lines to curves.
More free YouTube videos by Julie Harland are organized at http://yourmathgal.com
Questions answered by this video:
- What is the formal definition of a derivative?
- What does the derivative of a function tell you?
- How can you find the slope of a tangent line to a curve at a point on a curve?
- How do you find the derivative of a line?
- If f(x) = 3x - 2, what is f'(x)?
- How can you find the derivative of f(x) = 3x - 2 using the formal definition of a derivative?
- What is the derivative of f(x) = mx + b?
- If f(x) = 2 - x^2, how do you find f'(x) using the formal limit definition of a derivative?
- What is the slope of the tangent line to f(x) = 2 - x^2 at (0, 2) and (2, -2)?
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Staff Review
In this lesson, you will learn to find the derivative of a line using the formal limit definition of a derivative. There is one more example of finding the derivative of a quadratic equation as well. All steps are explained very well as they are in the whole series.
