In this initial video, we will review the Warm-Up Activity and introduce the idea of local linearity. Duration: 6:07

Here, we formally define local linearity. While we're on the subject of linear things, we will recap all the things we've learned about slope since Algebra 1. Remember when math was this simple? Duration: 10:29

Since nonlinear functions have variable slopes, we need a way to find the slope at a particular point on the graph. This introduces the Tangent Line Problem which birthed the branch of math known as Differential Calculus. Duration: 6:51

Drag point P to move the red dashed tangent line along the graph of y = sin x. To zoom in on the point of tangency, you will have to open the demo within desmos by click the words "edit graph on desmos" in the lower right corner.

In this video, we derive the slope of a secant line to a graph using a different quotient, and visualize how this secant line can help find the slope of a given tangent line. We will also introduce the second brand of Calculus, called Integral Calculus, which solved the classic Area Problem. Duration: 8:24

The purple line through PQ is a secant line to the graph of y = 0.25x^2. Drag point P closer to point Q to see how the secant line approaches the red dotted tangent line through point Q. The orange segment along the x-axis represents h within the difference quotient.

Unfortunately, the embedded graph below allows for minimal interaction. To change the number of rectangles used to approximate the area under the curve, open the graph within desmos by clicking on the words "edit graph on desmos" in the lower right corner. Now scroll down to pane 10 and use the slider to change the value of n.

After introducing limit notation to express the slope of a tangent line, we begin Investigation 1. Here you are tasked using local linearity to find the slope of the tangent line to y = sin x at x = π/2. Duration: 3:24

In this video, we debrief the results of Investigation 1, where we found the slope of the tangent line to y = sin ⁡x at x = π/2. In Example 3, you will similarly find the equation of the tangent line to y = x^2 at (1,1). Duration: 4:22

To conclude Objective 1, we review the solution to Example 3, the slope of the tangent line to y = x^2 at (1,1). Sometimes simply zooming in on a graph doesn't yield a terribly accurate slope value, so I will show you a more systematic way of approximating that slope using a series of secant lines that get progressively closer to the tangent line. Duration: 10:16