Curve Sketching: A Dying Art in AP Calculus . . .

Here's an old problem from the 1995 AP Calculus exam which emphasizes pre-calculus skills, particularly focusing on domain restrictions and graph sketching. Calculus techniques will be used AFTER the first part of the problem. I'll remind you of how to identify vertical and horizontal asymptotes, as well as how to analyze the function's behavior using derivatives and THE Chart. There is some slightly technical algebraic simplification done in the problem, so you'll want to make sure that you're comfortable with potentially wanting to do that(particularly whenever you are using the quotient rule with something involving a square root). I encourage you to review all of the concepts discussed, including domain restrictions as well as some algebraic methods we use for simplifying expressions such as limits. Give yourself a chance to try to work this out for yourself before watching this all through!

(ps -- in a test-setting, I would probably not use so much time developing context to the process of curve sketching, but I find that being thorough is more helpful in these instructional-type videos. It would not help you basically at all to just watch a dude speed through these AP problems and knock em each out in 5 minutes without explaining some of the tools that I'm able to use in my mind to solve them quickly; the point is to give you a few tools and show you how I think they would best be used. That being said, I do continue to try to keep these videos 15 minutes or less, which is the average amount of time per free response problem on the actual exam. Looks like this one went a bit over -- oh, well.)

0:00 Introduction
0:50 Domain Restrictions
5:00 Sketch the Graph
7:30 Using the Derivative to help Analyze
11:30 Finding Relative Extrema for the Sketch
14:30 Using Part (c) to help with Part (b)
18:40 Determining the Range

Видео Curve Sketching: A Dying Art in AP Calculus . . . канала MathfromtheVoid