Signature Assignment 2 Reflection

Signature Assignment #2 Reflection Mean Value Theorem By, Nania Platt

As to start off with, this assignment was fairly straightforward once I figured out what the assignment was asking for. I also took the time to break up the assignment into parts A-F to help me stay organized and to know where I was heading. I feel that the hardest part of this assignment was knowing what each section was asking, especially parts C and D. This is where the Mean Value Theorem was really applied and tested, I don’t think I fully understood what the theorem was until this assignment. The way that I combated the confusions and struggles was by looking again at my notes we took in class, looking at the textbook and online for answers on how to solve this problem. It wasn’t until I had solved the problem as we did it in class and analyzing the information I found that I realized that I had found the slope. The derivative of f(c) was the answer of the calculational process. Once I got to that point I was stumped what to do to move on, but when I was reminded that if you have a slope you need a point, and I had found two points as part C had asked for, they were (-3, -½) and (7, ¾). And using the point slope formula that we had used in previous chapters I could find the line segment that connects the two points on the f(x) function. Then by following the process in my notes I equaled the ⅛ slope I found to the derivative I found of the original function and found the values for c. Those values I plugged back into the original function to find the exact quadrants of the points for the tangent line segment. The tangent line segment was solved the same way with the same slope as before but this time it was parallel to the line segment and only touched the f(x) function by a point, (0, 0.4). How I knew this was, as I was solving my calculations I was graphing it on desmos. It helped to tell me if I was doing it right and if I was doing it wrong.

But through it all I figured out what the question was asking and got it finished. My next challenge was trying to write the Mean Value Theorem in layman's terms, I am still not sure if it is but I attempted to and finding a real world application was difficult too. I found one example online and cited my source, I hope that is ok. Overall I learned more how to input equations into the word document and what the Mean Value Theorem was the entire time. I have had some difficulty understanding what it meant before but not after some trial and error, I understand it, even if I can’t quite explain myself very clearly. I was also very pleased that I did not have to ask for help from any teacher or tutor, that I was able to find good sources and use my recall to complete this project. In the long run I learned a lot and hope to remember the process for the future.