Chapter Three: Section Six A summary of Curve Sketching

Chapter Three: Section Six A very simple slide ‘lecture’ here for this section. We have spent a few days now trying to tie together a couple of years of past knowledge with our new (still developing) understanding of the derivative of a function. The first and second derivatives can give us powerful clues about the physical behavior of a function.

Chapter Three: Section Six When we add this new knowledge to our ideas about how to find intercepts, how to find asymptotes (horizontal, vertical, and oblique), and what we know about the end behavior of functions, we can make very accurate sketches of complex functions. I want you to take some time to try the problem on the next slide and come to class prepared to discuss what went right and what went wrong in your attempt. Check your work with your calculator after you have made an honest attempt on your own.

Chapter Three: Section Six For the function to the right answer the following questions a) Identify any symmetries for this function (Is it an even function? Is it an odd function?) b) Identify the y -intercept(s) c) Identify the x -intercept(s) d) Identify the domain of the function e) Rewrite the function using long division or synthetic division f) Identify, with a sign chart, where the function is increasing and where it is decreasing g) Identify, with a sign chart, where the function is concave up and where it is concave down h) Identify any Max, min, or inflection points i) Identify the range of the function j) Identify any vertical or horizontal asymptotes k) Identify any oblique (slant) asymptote l) Use the information above to draw a rough sketch of the function.