A big part of this week was creating gifs with Desmos to demonstrate derivatives. Connor and I teamed up to do this task, but we really had no idea what we were doing at the beginning of the hour. However, we were able to broaden our way of thinking a bit and put variables as well as the functions of variables inside the slope to figure out how to get the slope to change. After that, all we had to do was shift the graph right 2 and up 2 to recreate the gif.
After that, we had to make a graph that no longer had a fixed point. What we did here was we shifted the graph using variables. This way, the point of intersection would no longer be fixed.
Finally, we had to create our own graph. We created a graph that had a line move along points on an increasing and decreasing sine function.
The activity at the beginning of the hour helped me understand that slope, that is rise over run, shifts at times and that sometimes it can be hard to pin down exactly where it is. I feel like getting this through my head was the biggest challenge for me since I was not used to seeing variables in the slope. That and I don't think I was fully awake Thursday morning either. The first graph had a translation by constants, for the second graph, we just replaced those constants with variables. The first two gifs were helpful because our own function was basically the second gif with a sine function in it. With it, we were able to create a graph that not only moves along up and down curves, but also narrow and wide curves as well. The analysis of the secant line is helpful because it's all about getting closer to the point. We may not have the exact tangent line, but the closer the secant line gets to the point, the closer we get to finding the tangent line, and we can make a much better approximation with it than without it.
After that, we had to make a graph that no longer had a fixed point. What we did here was we shifted the graph using variables. This way, the point of intersection would no longer be fixed.
Finally, we had to create our own graph. We created a graph that had a line move along points on an increasing and decreasing sine function.
The activity at the beginning of the hour helped me understand that slope, that is rise over run, shifts at times and that sometimes it can be hard to pin down exactly where it is. I feel like getting this through my head was the biggest challenge for me since I was not used to seeing variables in the slope. That and I don't think I was fully awake Thursday morning either. The first graph had a translation by constants, for the second graph, we just replaced those constants with variables. The first two gifs were helpful because our own function was basically the second gif with a sine function in it. With it, we were able to create a graph that not only moves along up and down curves, but also narrow and wide curves as well. The analysis of the secant line is helpful because it's all about getting closer to the point. We may not have the exact tangent line, but the closer the secant line gets to the point, the closer we get to finding the tangent line, and we can make a much better approximation with it than without it.