This week we did a desmos activity. At the beginning of the hour I had no idea what I was looking at. We fired up desmos and attempted up to recreate it to much difficulty. My group started with the equation f(x)=1/2x^2. We were then given the task of creating a line segment that would trace the line with a constant changing slope. This was challenging for me because I wasn't familiar with desmos and wasn't sure how to make a changing slope. We ended up choosing a point, which we named s, and f(s). We used the point slope equation y=(y2-y1)/(x2-x1)(x-x1)+y1 to get the equation for the first gif. Through this activity, I learned how to find the derivatives of a curve. I definitely struggled to figure out the first equation because I was unfamiliar with using the slope equation with variables. Changing from the first graph to the second my group just had to swap out the defined points for more variables. To make the last gif, I was already set up from my second graph, I just had to change the original f(x) equation. When the distance between s and w(my other point) gets infinitely small, you can find the derivative of the function.
CLICK HERE FOR MY GIFS
CLICK HERE FOR MY GIFS