Calc Prep Essentials: Filling the GAPs - Rate of Change or Slope (part 1): AskCalculusGeorge

Calc Prep Essentials: Filling the GAPs
This is the first video in this series to help those that are taking Calculus for the first time. The objective of this series of videos is to master key essential concepts from previous courses so that students can do well when they see these concepts in their Calculus class
Rate of Change or Slope (part 1):
1. In this video we talk about the general idea of a rate of change and use a common example of velocity (speed).
2. The objective is to think about the rate of change (or slope) graphically.
3. We mention average rate of change in this example for average velocity.
4. The average rate of change is also the slope of a secant line. We define a secant line as a line that passes through two points for a function.
5. Then, we talk about instantaneous rate of change and that instantaneous rate of change is the same as the slope of a tangent line. We define a tangent line as a line that intersects the function in one point that has the same direction or slope as the curve. We also mention in this example that this represents instantaneous velocity, which would be like looking at the speed on your speedometer at a particular instant.
6. Lastly, we mention the term derivative, which is a key concept for Calculus and is the same as the slope of a tangent line, or the same as the instantaneous rate of change.
7. We also mention how we compare slopes, and that we talk about that more in the next video.