Sections 1.3 and 2.1

Main Points: Section 1.3 talks about the average rate of change. It defines it as the rate of change of y between t=a and t=b as delta y / delta t, or [f(b) - f(a)]/ b-a. The average rate of change of a linear function is the slope, and the function is linear if the rate of change is the same at all intervals. This section also states that a function is increasing if f(x) increases as x increases, and is decreasing if f(x) decreases as x decreases. Furthermore, it talks about concavity. A function is concave up if it bends up from left to right (like a smiley!) and concave down if it bends down from left to right (like a sad face!). Finally, section 1.3 says that average velocity is the change in distance over the change in time. Section 2.1 opens by defining instantaneous velocity of an object at time = t as the limit of the average velocity of the object over shorter and shorter time intervals containing t. The instantaneous rate of change of f at a equals the limit of the average rates of change of a f over shorter and shorter intervals of a. The book then defines a derivitive of a function f at a, f ' (a), as the instantaneous rate of change of f at a. The derivitive of a certain point equals the slope of the function at the point as well as the slope of the tangent line of that point. Section 2.1 then discusses how to numerically and graphically estimate derivitives.

Challenges: Section 1.3 didn't give me many challenges because it basically reviewed a lot of what I learned in Calc last year. However, concavity could have confused people because it's definitely difficult to remember which is CCU and CCD. Section 2.1 was also a big review for me, but I still got a little confused remembering the difference between instantaneous rate of change and instantaneous velocity because they are so similar.

Reflections: This reading made me super happy because I love derivitives and am very excited to do them in class! I also really liked how they explained everything in these sections: it was much easier to understand than my highschool calculus book!