I recorded office hours yesterday morning with a handful of people from class who logged on. I went through the take-home exercises one by one, and we went through a number of examples from the textbook, the WebWork, and the Final Exam Review which are relevant for the take-home exam exercises. You can view the recording on Blackboard (toggle on the menu to “Recordings”):

https://bbhosted.cuny.edu/webapps/collab-ultra/tool/collabultra?course_id=_2317401_1&mode=cpview

I also scanned my notes from the office hours as a pdf and uploaded it to OpenLab Files.

Here is a summary of some relevant examples to study for each of the take-home exam exercises:

#1 (related rates): Final Exam Review (FER) #11-13, which we discussed in Class 27; see also Example 4.1 and the “Problem-Solving Strategy: Solving a Related-Rates Problem” from Sec 4.1 of the textbook.

#2 (linear approximation): See FER #8(a) and the example from Class 28, as well as the examples (and graphs) at the start of Sec 4.2. You can also review the exercises from Exams #1 and #2 where I asked you to write equations of tangent lines (and sketch them)

#3 (applied optimization): FER #9-10, which we covered in Class 26; I went through #9 again in office hours; see also Example 4.32 and the “Problem-Solving Strategy: Solving Optimization Problems” at the beginning of Sec 4.7.

#4 (limit definition of the derivative): See the solutions for FER #2(a)(b)

#5 (shape of the graph and maxima/minima using the 1st and 2nd derivatives): See the solutions for FER #18, which we discussed in class on Class 28; and the example we did in Class 25 (using a cubic function that appeared on Exam #1).

For the last exercise (and for #2, since it also involves sketching a graph) you should use Desmos or a graphing calculator to check your solutions and help you sketch an accurate graph.