Unit 4:  Applications of Differentiation

Unit 4:  Applications of Differentiation

COVID Era Unit 4 Videos

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• Day 37:  Intro to Implicit Differentiation (45)

  • • Revisit and Rework Today's Questions

    • 3.10:  9-26, 31-38 (not sure you can do this yet... maybe start it?)

• Day 38:  More Implicit Differentiation

  • • Rework the examples problems from today

    • 3.10:  9-26, 31-38

    • Short quiz next time on 3.10

• Day 39:  3.10 Requests, a Quiz, Start Related Rates

  • • Start the Take-Home Final (needs a tweak)

    • Video:  Book Example 1

• Day 40:  Related Rates (45)

  • • Watch Today's Examples Again

      • • Video:  Book Example 1

        • Video:  Book Example 2

        • Video:  Book Example 3

        • Video:  Book Example 4

    • 3.11:  1-25, 29-30, 33-34

      • • Selected Answers

    • Do you think you want to take the AB exam?  If so, buy a practice book and start working.  I can help during lunch.  I recommend:   (THIS ONE)

• Day 41:  Related Rates Workday

  • • Related Rates Worksheet

      • • Related Rates Worksheet Answers

        • 4 5 7 9 11

    • Video:  The 3 examples From BC

      • • 7 17 21

    • Document:  Fully Written up Examples from BC

    • Study for Friday's Related Rates Quiz

• Day 42:  Requests (45) and Related Rates Quiz (45)

  • • Do you think you want to take the AB exam?  If so, buy a practice book and start working.  I can help during lunch.  I recommend:   (THIS ONE)

    • Finish the related rates problems on the Take-Home Final

    • Don't forget everything over winter break!!

    • Go back through the Day 36 and Day 37 Notes on Implicit Differentiation (Question slide, Answer slide etc)

    • Watch the following Videos towards the end of the break

      • • Video 3:  Intro to Implicit Differentiation

        • Video 6:  Another Example

        • Video 7:  Harder Example

        • Video 8:  More Examples... a bit long

        • Video 1:  Four More Practice Problems

        • Video 2:  Answer 1

        • Video 3:  Answer 2

        • Video 4:  Answer 3

        • Video 5:  Answer 4

        • Video 6:  Those Formulas from 3.8 and 3.9

        • Video:  Book Example 1

        • Video:  Book Example 2

        • Video:  Book Example 3

        • Video:  Book Example 4

• Day 43:  Remember Related Rates? (45)

  • • Rework the Quiz

• Day 44:  Extrema, Increasing and Decreasing 

  • • Finish the examples in Today's Notes

    • 4.2:  21-23, 29-41 odd, 47, 55

      • • 21 39 41

        • 45 47

• Day 45:  Mean Value Theorem, Concavity and Inflection Points

  • • Watch These Videos:

      • Video 1:  Mean Value Theorem Example

      • Video 2:  More Thoughts on the Mean Value Theorem

      • Video 3:  One More MVT Example

    • 4.3:  1-7 odd, 15-17, 23, 25, 29, 31, 35-39 odd, 49

      • • 3 7 25 29

        • 31 49

    • Watch These Videos Too:

      • Video 1:  Tying Stuff Together

      • Video 2:  One More Of Those, but with Trig

      • Video 3:  Today's Notes

      • Video 4:  Points of Inflection

      • Video 5:  A Full Problem Part 1

      • Video 6:  A Full Problem Part 2

      • Video 7:  One More of Those, but with Trig

    • 4.4:  1, 3-17 odd, 20-22, 39-47 odd, 51, 54-56

      • • 4.3:  #37 Full Write-up

        • 4.4:  #45 Full Write-up

        • 4.4:  #51 Full Write-up

        • 4.6:  #29 Full Write-up

        • 4.6:  #43 Full Write-up

• Day 46:  Requests (45)

  • • Get Caught Up

    • Examples of Curve Sketching

      • • 4.3:  #37 Full Write-up

        • 4.4:  #45 Full Write-up

        • 4.4:  #51 Full Write-up

• Day 47:  L'Hospital's Rule

  • • Video 3:  Proof of L'Hopital's Rule

    • 4.5:  1-15 odd, 19, 21, 25-29 odd, 33-37 odd

    • 4.6:  13, 17, 25, 29, 41, 43

• Day 48:  Requests/Workday

  • • Examples of Curve Sketching

      • • 4.3:  #37 Full Write-up

        • 4.4:  #45 Full Write-up

        • 4.4:  #51 Full Write-up

        • 4.6:  #29 Full Write-up

        • 4.6:  #43 Full Write-up

    • Quiz Next Time on Curve Sketching

• Day 49:  Tons of Requests (70), Shape of Curves Quiz (20)

  • • Finish 6 of the 8 problems on the Take-Home Final

    • Redo and Rework a few of Related Rates Worksheet

    • Redo and Rework a few of 4.5:  1-15 odd, 19, 21, 25-29 odd, 33-37 odd

    • Redo and Rework a few of 4.6:  13, 17, 25, 29, 41, 43

    • Examples of Curve Sketching

      • • 4.3:  #37 Full Write-up

        • 4.4:  #45 Full Write-up

        • 4.4:  #51 Full Write-up

        • 4.6:  #29 Full Write-up

        • 4.6:  #43 Full Write-up

• Day 50:  Optimization (75)

  • • Videos for today

      • • Video 1:  Optimization Example 1

        • Video 2:  Optimization Example 2

        • Video 3:  Optimization Example 3

    • 4.7:  1-9, 11-13 (approximate only on #13), 23, 33

      • • 1 3 5

        • 7 9 11

        • 13 33

        • Video 1:  4.7 #2 Video 2:  4.7 #4

        • Video 3:  4.7 #6a Video pi:  4.7 #6b

        • Video 4:  4.7 #8 Video 5:  4.7 #12

    • Do you think you want to take the AB exam?  If so, buy a practice book and start working.  I can help during lunch.  I recommend:  (THIS ONE)

• Day 1:  Workday/Requests (45)

  • • Review for the Test:

      • Pick a few problems from each of:

        • 3.10:  9-26, 31-38

        • 3.11:  1-25, 29-30, 33-34

        • Related Rates Worksheet

          • • Related Rates Worksheet Answers

        • 4.2:  21-23, 29-41 odd, 47, 55

        • 4.3:  1-7 odd, 15-17, 23, 25, 29, 31, 35-39 odd, 49

        • 4.4:  1, 3-17 odd, 20-22, 39-47 odd, 51, 54-56

        • 4.5:  1-15 odd, 19, 21, 25-29 odd, 33-37 odd

        • 4.6:  13, 17, 25, 29, 41, 43

        • See Day 48 for a selection of curve sketching examples

        • 4.7:  1-9, 11-13 (approximate only on #13), 23, 33

    • Optimization Quiz Wednesday.

• Day 2:  Requests (70), Optimization Quiz (20)

  • • Redo Day 50 Homework

    • Take Home Test due NEXT TIME NO EXCUSES!!!  Feel free to turn it in early!

    • Go to the end of chapter 3 in your book and do "Preparing for the AP Exam" (pages AP 3-1 to AP 3-3 ): 15-18, Free Response Question (FRQ) 2-4 

    • Go to the end of chapter 4 in your book and do "Preparing for the AP Exam" (pages AP 4-1 to AP 4-4 ): 2-6, 9-10, 14-16

    • Do you think you want to take the AB exam?  If so, buy a practice book and start working.  I can help during lunch.  I recommend:   (THIS ONE)

• Day 3:  Applications Last Requests, Math 251 Take-Home Final Due (45)

  • • Redo Day 51 Homework, except you can skip the 2nd one...

• Day 4: Derivative Applications Test

  • • No Homework!