The Gifs link is below:
https://docs.google.com/document/d/181n0S0oojOvfkapUKzq_TRpmjZRoHA_pGcniusD10uE/edit?usp=sharing
This week we learned about derivatives through a gif creation exercise. We were working with the equation f(x)= .5x^2 on an application called desmos. It was somewhat confusing at the beginning of the hour when trying to organize the gifs, but we managed to figure it out. We had to construct line segments that traced another line with an always changing slope. This kind of played into our prior worksheet that dealt with the speed of a car on an interval of time. Both situations called for finding a limit for the incalculable. To make our graphs we used the point slope equation: y=(y2-y1)/(x2-x1)(x-x1)+y1. We then plugged in points s and f(s) to form the first gif.This actively introduced me to derivatives and although I find the process a bit confusing still, the reasoning behind it all makes sense. When working on the second gif my group exchanged the s and f(s) points for letter variables (to allow two moving points). This was good, because I struggled understanding the first gif in the beginning, but seeing the same idea at work in different settings made the entire derivatives concept more manageable. To make the last gif, we just used the same graph but a different f(x) equation. From this activity I learned that the secant line makes it easier to guess the tangent line and get a more accurate answer. Overall, I'm looking forward to seeing what next week brings.
https://docs.google.com/document/d/181n0S0oojOvfkapUKzq_TRpmjZRoHA_pGcniusD10uE/edit?usp=sharing
This week we learned about derivatives through a gif creation exercise. We were working with the equation f(x)= .5x^2 on an application called desmos. It was somewhat confusing at the beginning of the hour when trying to organize the gifs, but we managed to figure it out. We had to construct line segments that traced another line with an always changing slope. This kind of played into our prior worksheet that dealt with the speed of a car on an interval of time. Both situations called for finding a limit for the incalculable. To make our graphs we used the point slope equation: y=(y2-y1)/(x2-x1)(x-x1)+y1. We then plugged in points s and f(s) to form the first gif.This actively introduced me to derivatives and although I find the process a bit confusing still, the reasoning behind it all makes sense. When working on the second gif my group exchanged the s and f(s) points for letter variables (to allow two moving points). This was good, because I struggled understanding the first gif in the beginning, but seeing the same idea at work in different settings made the entire derivatives concept more manageable. To make the last gif, we just used the same graph but a different f(x) equation. From this activity I learned that the secant line makes it easier to guess the tangent line and get a more accurate answer. Overall, I'm looking forward to seeing what next week brings.