The activity at the beginning of the hour where we had to find/estimate the slope of a point on a line was very important in helping me understand the general idea of the first gif. This is because it allowed me to see how the tangent and secant lines would be used in figuring out that specific slope. The first gif represents this by showing all of the secant lines leading to the tangent line that includes the one fixed point, and how the slope slowly changes and is slightly different at every point. Here is the first gif: https://drive.google.com/file/d/0B9SIejrlItGYYVRIZUYySVg1OEU/view?usp=sharing
At first, Austin and I had trouble just figuring out how to work Desmos in general. We really didn't know how any of it worked, and we especially had trouble figuring out how to make a slider. Then once we got the hang of the basic ideas, we struggled with figuring out what variables to use where, just because there were so many letters and it kind of got confusing. We overcame these problems by just trying things out and moving things around, while also thinking about the math behind it.
A change we made from the first gif to the second was that the first gif had a fixed point with a slider that moved along the line, while the second gif had two sliders and no fixed points. The second gif had to have the second function (slope line) filled with the two letters used in the sliders where as the first gif had numbers in it corresponding with the fixed point. Here is the second gif: https://drive.google.com/file/d/0B9SIejrlItGYbE5uUFU1Vjc5ZlU/edit?usp=sharing
The setup for the first two gifs helped with the creation with our own function (third gif) by helping us to understand how to make the slope of the second function (the secant/tangent line) in relation to the original function. Here is the third gif:
https://drive.google.com/file/d/0B9SIejrlItGYQVhKMldpWExfNkk/edit?usp=sharing
The analysis of secant lines helps us to determine the tangent line of the function because as you approach a fixed point on the function, the secant line can help give a better approximation of the tangent line at that specific point.
A change we made from the first gif to the second was that the first gif had a fixed point with a slider that moved along the line, while the second gif had two sliders and no fixed points. The second gif had to have the second function (slope line) filled with the two letters used in the sliders where as the first gif had numbers in it corresponding with the fixed point. Here is the second gif: https://drive.google.com/file/d/0B9SIejrlItGYbE5uUFU1Vjc5ZlU/edit?usp=sharing
The setup for the first two gifs helped with the creation with our own function (third gif) by helping us to understand how to make the slope of the second function (the secant/tangent line) in relation to the original function. Here is the third gif:
https://drive.google.com/file/d/0B9SIejrlItGYQVhKMldpWExfNkk/edit?usp=sharing
The analysis of secant lines helps us to determine the tangent line of the function because as you approach a fixed point on the function, the secant line can help give a better approximation of the tangent line at that specific point.