Here are the main points that are addressed in the video. Please read these and think about them as you watch.

• The slope of a line secant to a graph of a function $y = f(x)$ is equal to the average rate of change of $f(x)$ with respect to $x$ over the interval of $x$-values at which the secant line intersects the graph of the function.
• The line tangent to a graph of a function at a particular point is a representation of the local linearity of the function at that point. As such, the slope of the line tangent to the graph of a function is equal to the value of the derivative at the point of tangency.
• The slope of the line tangent to a function $y = f(x)$ represents the number of times that $dy$ is larger than $dx$, where $dy$ and $dx$ represent infinitesimal changes of $y$ and $x$ respectively.