Author: Suman Ganguli (Page 2 of 12)

Schedule

WebWork: “Derivatives – Logarithmic” and “Derivatives – Implicit” extended to Fri Dec 13
Exam #3:
- the take-home exercises for 50% of this exam were handed out in class, to be handed in on Monday Dec 16
  - see this post for an outline of the topics covered in the take-home exercises
- there will also be a short in-class exam on Monday Dec 16, for the remaining 50%; these exercises will be similar to the take-home exercises
Final Exam Review— hand in written solutions to the following exercises (either on Monday with Exam #3, or on Wednesday before the Final Exam):
- #5 (logarithmic differentiation)
- #7 (implicit differentiation)
- #8 (tangent lines, linear approximations and differentials)
- #16 & #17 (optimization)
- #18 (using critical pts, intervals of increasing/decreasing, and intervals of concavity for sketching a graph)
  - we set up most of these in class, and/or did similar examples
  - the Final Exam Review exercises (including limited solutions) is available as a pdf on OpenLab Files
Final exam: Wednesday Dec 18

Boardshots

.We completed the applied optimization example we had started on Monday (FER #17), and then did a related rates example (FER #12).

Exam #3 – take-home exercises

December 12, 2024 / Suman Ganguli

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.

Class 27 Recap (Mon Dec 9)

December 10, 2024 / Suman Ganguli

Schedule

WebWork: “Derivatives – Logarithmic” and “Derivatives – Implicit” extended to Fri Dec 13
Exam #2 corrections (optional) are due tomorrow (Wed Dec 11)
Final Exam Review– hand in written solutions to the following exercises (on Wed Dec 11 if you have them finished, but if you need more time I will take them next week as well):
- #5 (logarithmic differentiation)
- #7 (implicit differentiation)
- #8 (tangent lines, linear approximations and differentials)
- #16 & #17 (optimization)
- #18 (using critical pts, intervals of increasing/decreasing, and intervals of concavity for sketching a graph)
  - note that we set up #8 and #17 in class (see below), and we set up #5 and #7 last week
  - for #18, follow the example we did in class last Wednesday, and recapped in this class (see below)
  - the Final Exam Review exercises (including limited solutions) is available as a pdf on OpenLab Files
Exam #3:
- this will cover the topics from the Final Exam Review listed above (plus related rates, which we will cover tomorrow)
- take-home exercises for 50% of this exam will be handed out in class on Wed Dec 11, to be handed in on Monday Dec 16
- there will also be a short in-class exam on Monday Dec 16, for the remaining 50%; these exercises will be similar to the take-home exercises
- we will use half the class period on Mon Dec 16 to do some additional review for the final
Final exam: Wednesday Dec 18

Boardshots

We recapped the examples previous class on graph-sketching using the first and second derivatives, looking at a cubic polynomial f(x). We discussed these figures from Sec 4.5 which illustrate these concepts: