Main Ideas

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Here are the main points that will be addressed in the videos. 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 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 (which does not need to be a whole number) that $dy$ is larger than $dx$ , where $dy$ and $dx$ represent infinitesimal changes of $y$ and $x$ respectively.