The Universe of Functions and Derivatives

This spring term I have been taking an introductory calculus course. Over these past few weeks we have reviewed basic knowledge like slope formula and functions in order to be able to apply them into the math we would be doing in calculus. Once we finished reviewing we started off with learning about derivatives and finding them using limits (change in x as it approaches 0). Once we got comfortable with it we discovered there was short cut that led us to our derivative quicker, the power rule. Using the power rule we could find the derivative without having to go through all the steps like we did when using limit notation. Finally it was time to put our new knowledge to use and evaluate a function of our very own choosing. I chose my function and evaluated it in various ways. Below is a slideshow showing how I did it step by step. Enjoy!

In conclusion I really enjoyed working on this project although it proved to be a challenge to me at the beginning since I chose a function that did not work very well with the power rule in its original form. In the end I learned a lot about functions, derivatives, power rules, and instantaneous slope and I feel ready to move into unit 2 of my calculus course.