Sections 2.2 and 2.3

Main Points: Section 2.2 defines the derivitive as f ' (x) = the instantaneous rate of change of f at x. It also states that a person can can tell if a function is increasing or decreasing by looking at the graph of the derivitive. For example, if the sign of the derivitive is greater than zero at a certain interval, it is increasing. The same goes for negative and decreasing, as well as zero and constant. Also, if f ' is large in magnitude, f is steep, and if f ' is small in magnitude, f is gently sloping. The book also gives examples on how to estimate a derivitive numerically. Section 2.3 gives alternate ways of stating the derivitive of a function, such as f ' (x)= delta y/ delta x, dy/dx. and d/dx (y). It is also important to remember that derivitives are much like slope in that they are composed in the manner of rise over run. The units of a derivitive are the units of the dependent variable over the units of the independent variable. Also, the derivitive of velocity equals acceleration, with the units being the length unit / (time unit ^2). The derivitive can also help estimate the values of a function. The book states that the local linear approximation of a function is: delta y is about equal to f ' (x)*delta x for delta x near zero.

Challenges: In section 2.2, I did not understand the ways to improve numerical estimating of a derivitive. The book explained it really bizzarrely and I couldn't comprehend it. Also, I didn't understand why the book was going in such a round about way to explain the derivitive, especially in the last example. Section 2.3 didn't really give me any problems but the different ways of how to state the derivitive could have confused a student who has never taken calculus or worked with derivitives before.

Reflections: This is still all kind of a big review for me, but I love derivitives so it's okay! My only problem is that the book takes somewhat simple concepts and explains them in super weird ways which totally throws me off! I really liked how the authors explained how to choose the units for derivitives though - I used to become confused on units when I took Calculus last year.