Thursday, July 23, 2026

MAT122 SSII 2026 Week 4: Derivative Applications

   

My HS Classroom running Linux 1994-2019
AP Calculus AB/BC 1993-2018
AP CSA/CSAB 1988-2019
NYS Regents Math & Physics 1984-2020

MAT122 SSII 2026 Week 4: Derivative Applications

Dear Students,

This week we investigated several applications of the Derivative! We introduced derivatives of sin(x), cos(x) using the Difference Quotient and tan(x) using the Quotient Rule. We used our understanding of Inverse Functions coupled with Implicit Differentiation and the Chain Rule to find derivatives for ln(x), arctan(x), arcsin(x) and arccos(x). We even talked about L'Hopital's Rule.




Then we developed the idea of Optimization. We introduced the 1st Derivative Test, the 2nd Derivative Test and the Closed Interval Test aka the Min/Max Theorem aka the Candidates Theorem. We even got to work a few Related Rates problems!

After all that, we started Unit 5 early dealing with Anti-Derivative Functions and Area. We played with some Riemann Sums and even wrote a TI-BASIC programs called LRTE.BAS to estimate these sums as LeftSum, RightSum, TrapSum & TrapError. Wow!


Please see WEEK04 notes on our Google Drive and our Screencasts on BrightSpace & YouTube!


Last, but not least, here's this week's Filks! We start each class with a fun Filk or short Documentary related to a specific topic we're learning in class or something related to STEAM.







That's it for now. Enjoy your weekend!

Well, that's all folks!

Be well,

A. Jorge García

Applied Math, Physics & CompSci

Nassau Community College (1993-)

http://shadowfaxrant.blogspot.com

http://www.youtube.com/calcpage2009


Baldwin High Retired (1984-2020):

Computing Independent Study Facilitator

Continental Mathematics League Advisor

Baldwin High Chess Club Founder 

Baldwin High Chess Team Coach:

US Chess Federation Affiliate: BHCC

National CompSci Honor Society Advisor: 

Grace Hopper NY Chapter

2017 PAEMST NYS Secondary Math Nominee: 

https://www.paemst.org


HTH,

A. Jorge Garcia

Teaching With Technology:
Coding since 1975,
NYS Regents Math & Physics since 1984,
College Math & CompSci since 1993,
 Linux Clusters since 2002,
CAS since 2011,
SemiRetirement since 2020!
What's in store for 2029?
 
AP Computer Science: 1988-2019
AP Calculus BC: 1993-2018 
Applied Math, Physics and CS

Please support my classroom:
www.patreon.com/calcpage2020

https://www.udemy.com/user/alvar-garcia-fernandez

calcpage.redbubble.com

https://www.ebay.com/usr/sffbclub  



2017 NYS Secondary Math PAEMST Nominee

pastebin youtube slideshare

(IDEs & Code)
MATH 4H, AP CALC, CSH: SAGECELL
(Curriculae)
CSH: CodeHS
APCSA: Big Java
APCSA: CSAwesome
APCSA: AP Central

RECOMMENDED AP COMPSCI REVIEW:
CRIB SHEET (no longer given during exam)
FREE TEXTBOOKS
REVIEW BARRONS ONLINE 
REVIEW APCENTRAL (exam format)
REVIEW EDX REVIEW MOOC01 
REVIEW UDEMY REVIEW MOOC02 
REVIEW CODING_BAT  
AUDIT CS50

RECOMMENDED AP CALCULUS REVIEW:
CRIB SHEET (not given during exam) 
REVIEW BARRONS ONLINE 
REVIEW APCENTRAL (AB exam format)
REVIEW APCENTRAL (BC exam format)
REVIEW APCENTRAL (AB exam questions)
REVIEW APCENTRAL (BC exam questions)
REVIEW EDX MOOC01 
REVIEW COURSERA MOOC02

XTRA CREDIT FILKS RUBRIC 
(1 video = up to 5 bonus points):
1) Use a recognizable tune.
2) Karaoke entire song changing up the words (about STEAM).
3) You are Singing, Dancing or Playing an instrument.
4) You upload your video to YouTube and provide the url.
5) YouTube Description includes the lyrics.

XTRA CREDIT ARTICLES RUBRIC
(up to 5 articles = 1 bonus point each):
1) Cover Sheet is a Summary of the article.
2) FullPage, 12 pt, DoubleSpaced, 1" Margin.
3) Article has to be STEAM related
4) Article has to be a current event.
5) Copy of entire article is attached.

NOTE TO READER:
In recent years our independent study class has been about the care and feeding of Linux Clusters: How to Build A Cluster, How To Program A Cluster and What Can We Do With A Cluster? 

BTW, Shadowfax is the name of the cluster we build! FYI, we offer 4 computing courses: 

CSH: Computer Science Honors with an introduction to coding in Python using SAGE, IDLE, VIDLE and Trinket, 

CSA: AP Computer Science A using CS50, this IDE and this IDE and OpenProcessing, 

CSI: Computing Science Independent Study using OpenMPI and 

CSL: Computing Science Lab which is a co-requisite for Calculus students using Computer Algebra Systems such as SAGE.

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CIS(theta) aka CSI
Membership Hall Of Fame!

CIS(theta)* 2020-2021: 
DiegoM(12), GeordiP(12), MattB(12), MattO(12), MelanyeCG(12), NickE(12), WilliamF(12)
*Honorable Mention: I retired before we got to start our project this year...

CIS(theta) 2019-2020:
AaronH(12), AidanSB(12), JordanH(12), PeytonM(12)

CIS(theta) 2018-2019:
GaiusO(11), GiovanniA(12), JulianP(12), TosinA(12)

CIS(theta) 2017-2018:
BrandonB(12), FabbyF(12), JoehanA(12), RusselK(12)

CIS(theta) 2016-2017: 
DanielD(12), JevanyI(12), JuliaL(12), MichaelS(12), YaminiN(12)

CIS(theta) 2015-2016: 
BenR(11), BrandonL(12), DavidZ(12), GabeT(12), HarrisonD(11), HunterS(12), JacksonC(11), SafirT(12), TimL(12)

CIS(theta) 2014-2015: 
BryceB(12), CheyenneC(12), CliffordD(12), DanielP(12), DavidZ(12), GabeT(11), KeyhanV(11), NoelS(12), SafirT(11)

CIS(theta) 2013-2014: 
BryanS(12), CheyenneC(11), DanielG(12), HarineeN(12), RichardH(12), RyanW(12), TatianaR(12), TylerK(12)

CIS(theta) 2012-2013: 
Kyle Seipp(12)

CIS(theta) 2011-2012: 
Graham Smith(12), George Abreu(12), Kenny Krug(12), Lucas Eager-Leavitt(12)

CIS(theta) 2010-2011: 
David Gonzalez(12), Herbert Kwok(12), Jay Wong(12), Josh Granoff(12), Ryan Hothan(12)

CIS(theta) 2009-2010: 
Arthur Dysart(12), Devin Bramble(12), Jeremy Agostino(12), Steve Beller(12)

CIS(theta) 2008-2009: 
Marc Aldorasi(12), Mitchel Wong(12)

CIS(theta) 2007-2008: 
Chris Rai(12), Frank Kotarski(12), Nathaniel Roman(12)

CIS(theta) 1988-2007: 
A. Jorge Garcia, Gabriel Garcia, James McLurkin, Joe Bernstein, ... too many to mention here!

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