Derivatives and Tangent Lines 2

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Taught by YourMathGal
  • Currently 4.0/5 Stars.
2069 views | 3 ratings
Part of video series
Meets NCTM Standards:
Lesson Summary:

This lesson builds upon the previous lesson on derivatives by introducing tangent lines to curves. The concept of secant lines is used to approximate the slope of the tangent line at a given point, which can be made more precise by taking the limit as the distance between the two points approaches zero. The formula for the slope of the tangent line is introduced, and an example problem is solved step-by-step to find the slope of the tangent line to a given curve at a specific point. By the end of the lesson, viewers will have a solid understanding of how to calculate the slope of tangent lines to curves.

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:
  • How do you find the slope of the tangent line of f(x) = x^2 - 3 at (1, -2)?
  • How can you use limits and the formula for slope to find the exact slope of the tangent line at a point on a curve?
  • If you have a graph y = f(x), how do you find the slope between (c, f(c)) and (c + h, f(c + h)) if c is very small?
  • How do you derive the formal definition of a derivative?
  • What is the formal definition of a derivative?
  • What is the definition of a tangent line with slope m?
  • How do you find the limit as h goes to 0 of (f(1 + h) - f(1))/h?
  • How do you find the slope of a tangent line by using the formal limit definition of a derivative?
  • What is the limit as h goes to 0 of 2 + h?
  • Staff Review

    • Currently 4.0/5 Stars.
    This lesson goes into depth with tangent lines and derives the formula for a derivative by using a secant line between two points that are very close to each other on a curve. The formal definition of a derivative is introduced and explained as well.