1.3 Rates of Change and 2.1 instantaneous rate of change

Main points
The average rate of change is determined by the change in y divided by the change in time for a given data set. A function is increasing if f(x) increases with x. The opposite is true for decreasing functions. The average rate of change between two points of a function is represented by a line connecting the two points. This line is called the secant line. concave up and down refer to which way a function "opens up." The average change in position with respect to time is also known as velocity. Speed is the magnitude of a velocity without respect to direction. Instantaneous velocity is the limit of the average velocity of the object over shorter and shorter time intervals containing (t) time. Instantaneous rate of change is similar except that it is basically a measure of the slope of a function over shorter and shorter intervals. The derivative of a function at point a is the instantaneous rate of change.

Challenges
I had a hard time distinguishing between instantaneous velocity and instantaneous rate of change. I realized that they are actually the same. Yeah I feel stupid. Velocity is a rate of change or basically the slope of a function.

Reflections
I'm used to finding the derivative in the good ol bring the exponent out front and subtract one from that method. It's good to see this method again to see how to "manually" come up with a derivative, it connects the process with its roots, at least for me.