GATech: Survey of Calculus (Math 1712): Topics for week 6

MATH 1712: WEEK 6

Determine the intervals on which a function is increasing, decreasing, concave up, and concave down
Find all vertical and horizontal asymptotes of a function
Sketch a graph of the function using the first- and second-derivative tests

Text coverage: Sections 4.1 - 4.3 of S. Tan.

Week 6 Formula Sheet
Week 6 Practice Problems
Maple worksheets
- Curve Sketching: This worksheet takes the reader through all the steps of the curve sketching process using Maple commands.
- Plotting Graphs: One of the primary uses of the computer will be to give visualization. This worksheet gives syntax for plotting graphs. The worksheet does not use the calculus. Rather, it is an introduction to techniques for plotting graphs with Maple.
- Interpreting Graphs: The goal of this worksheet is to understand the graph of the following function: > h:=x->(x^3+3*x-5)/(x^2+2); Although you can just plot it in Maple, we want to do this systematically to get a better idea what to look for when looking at the graph. Read each question, and try to see if you could have guessed this by looking at the graph of the function.
- The Year of the Fastest Growth for the US Population: The U. S. Constitution requires a census every ten years. We provide a "Logistic Fit" for that data and graph the fit superimposed with the data. This worksheet then asks the following question: In what year does this logistic fit suggest the fastest growth in the U. S. census data?
Java Projects
- Plotting Functions: This Java project(external link) is for plotting functions which do not have singularities and the axes are fixed at the center of the window and do not represent any values of x or y.