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

#1 (implicit differentiation): Final Exam Review (FER) #7; see also the example we did in Class 24 and Class 25, the WebWork exercises, and Sec 3.8.

#2 (related rates): Final Exam Review (FER) #12, which we discussed in Class 28; see also Example 4.1 and the “Problem-Solving Strategy: Solving a Related-Rates Problem” from Sec 4.1 of the textbook.

#3 (linear approximation): See FER #8(a), which we did in Class 27, 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).

#4 (applied optimization): FER #10 & #17; we covered the latter in Class 27 and Class 28 . See also the “Problem-Solving Strategy: Solving Optimization Problems” at the beginning of Sec 4.7.

#5 (shape of the graph and maxima/minima using the 1st and 2nd derivatives): See the solutions for FER #18, and the example we did in Class 26 and Class 27.

For the last exercise (and for #1 and #3, since they also involve graphs) you should use Desmos or a graphing calculator to check your solutions and help you sketch an accurate graph.