Concavity, Inflection Points, and Second Derivative

This calculus video tutorial provides a basic introduction into concavity and inflection points. It explains how to find the inflections point of a function using the second derivative and how to find the intervals where the function is concave up and concave down using a sign chart on a number line. When the second derivative is positive, the function is concave up which means the first derivative is increasing. When the second derivative is negative, the function is concave down which indicates that the first derivative is decreasing.
Introduction to Limits:
• Calculus 1 - Introduct...
Derivatives - Fast Review:
• Calculus 1 - Derivatives
Introduction to Related Rates:
• Introduction to Relate...
_____________________________
Extreme Value Theorem:
• Extreme Value Theorem
Finding Critical Numbers:
• Finding Critical Numbers
Local Maximum & Minimum:
• Finding Local Maximum ...
Absolute Extrema:
• Finding Absolute Maxim...
Rolle's Theorem:
• Rolle's Theorem
________________________________
Mean Value Theorem:
• Mean Value Theorem
Increasing and Decreasing Functions:
• Increasing and Decreas...
First Derivative Test:
• First Derivative Test
Concavity & Inflection Points:
• Concavity, Inflection ...
Second Derivative Test:
• Second Derivative Test
_________________________________
L'Hopital's Rule:
• L'hopital's rule
Curve Sketching With Derivatives:
• Curve Sketching - Grap...
Newton's Method:
• Newton's Method
Optimization Problems:
• Optimization Problems ...
_______________________________________
Final Exams and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

[@TheOrganicChemistryTutor]

Next Video: czcams.com/video/G8GAsYkZlpE/video.html
Final Exams and Video Playlists: www.video-tutor.net/

[@derreck1149]

O

[@symonequinzon6384]

10 min vid> 10 hours of discussion.
Thank you sir.

[@HikmatShahi-to3vk]

❤

[@Belle-is9hu]

I'm watching all the ads to their entirety because this man needs it. He's saving my Calculus grade, so he deserves the revenue.

[@PhuongNguyen-gx6ez]

I think if u click in the ads, he will get more money.

[@schoolofenlightenment8449]

Can skipping ads decrease amount?

[@rubiebenke3071]

On god

[@mact.4778]

No cap

[@RaffaelloLorenzusSayde]

Stop honoring him 👍

[@edgarrubio5231]

organic chem, physics, and now calculus. id give you my tuition money if i your videos have made my life much, much easier

[@nononono-lm8id]

This guy is literally a god. Saves so many lives. Think about how much this man has contributed to society by helping so many people and helping people achieve their goals! Thanks JG

[@jafernoorani2190]

Thank you so much. You have really saved my life. I am a senior taking AP Calc but I have been watching your videos since geometry and I honestly wouldn't be where I am today if it wasn't for your videos. thank you man much appreciated

[@dalaibrahim]

same, currently. did you get a good score?

[@ddahstan6876]

Reading textbook material puts me to sleep honestly. This man's writing the textbook for us interactively and concisely. Many of us can't thank you enough!!!

[@abdulharrison4380]

I'd like to meet you Sir. You're a god of a teacher.

[@GGW34]

I am sick and in pain, I am tired, and I have calculus and chemistry tests tomorrow, and I might also have a West Civ test too (trust me, that's the hardest one, that teacher is a sociopath). You are literally the only reason why I am not dropping out of high school rn.

[@ayansuleymanova03]

I just wan to thank from the bottom of my heart! I watched all calculus 1 videos and to revise everything what I have learned so far at university and you videos really helped me a lot in the last a few days. you are AMAZING!

[@sierra117420]

I actually love you man. Your videos have been extremely helpful even when I'm in 2nd year Uni and have to revise basic concepts in as less time as possible.

[@yeabsraamare6615]

you made all the subjects not like science but pure ART! That is the kind of instructors this world needs

[@braydonpaulse]

Much love and more life to this legend. Thanks for making me pass calculus.

[@annashaji3267]

Thank you sir for teaching this topic within few minutes....its is really helpful in this quarantine time...once again thank you so much

[@rakeshkhanna7253]

I was able to understand well the lecture fairly well. Thanks!

[@user-ov4so9ty9d]

The home of team last minute 😂🫡you deserve a medal Sir 👏

[@tanzimtihan9686]

You're a real life hero, salute

[@Enter54623]

Thanks for this, haven’t watched the video but the thumbnail is enough for me to sure I got the question right on my calc final lmao

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for a solid analysis and deep explanation of Concavity, Inflection Points and the Second Derivative Test in Calculus One. Solving problems will only increase my overall knowledge and understanding of this material in Calculus. This is an error free video/lecture on CZcams TV with the Organic Chemistry Tutor.

[@alondram.colonvega812]

You're videos always hit the points i have doubt in, how do you do it? I don't know but you out here saving me, man. Thank u so much!!

[@golammashrafilabib3192]

Watching this before my mid term exam! To the point explanation! Thanks.

[@musicatation2254]

You are the best sir,you’ve taught me more than college

[@karinaburgess3989]

LITERALLY BEST RESOURCE OUT THERE FOR MATH.

[@Berserkerishim]

Thank u, got 100% for my calculus test bcoz of uu

[@ManoOorii]

you're literally my savior

[@articcircleado]

Thanks again --- Seriously I really appreciate your help.

[@littleWormGirl]

i hope you know how much of an impact these videos make! You're the reason I'm passing calculus :-)

[@anigadariya1524]

I’d pay you instead of my math college professor dude, thank you so much

[@cybersegs]

Man you deserve billion dollars for your service

[@chenliang1112]

my calculus teacher is good at explaining things, but you're even better👍

[@pratyush2331raj]

Thankyou Sir for your wonderful, helpful, short-videos....😯😮
It helps me a lot....😊

[@real.rafi.ahamed]

thank you so much for this free teaching
it saved my calculas grade

[@lilithasotondoshe8226]

always clear
thank you Sir.

[@PodcastsShorts69421]

You are honestly a life saver

[@akshattomar6100]

this guy is just insane, saves from from falling apart many times.....

[@vhbeghini]

Dude your videos are excelent, really. Thank you so much.

[@jareenc6066]

this man single handedly saving my college grades

[@FroZenMystic1]

Thanks once again, this video was so helpful.

[@nadiahulwat.1788]

Thank you so much for sharing your knowledge, i appreciate it so much sir.

[@angel.diaz22]

I have a B in Calculus right now because of him. Thank you for everything!!

[@meerabfatima2952]

Great sir.......
U are such a great teacherr

[@pumpkinperson9365]

THE HERO OF MY HW!!

[@batungamilitebelelo666]

THATS A MARVELOUS TUTOTIAL

[@muhammadsohail5373]

Thnkuuuu soooo much sir for making it easy that we can understand .😍😍😍😘😘😘😘

[@hamoodibeats1944]

Thanks mann!! Easy and cool way of explaining, despite our clowns in the university 😂🙌🙌

[@anikeshsharma6888]

Great helped me a lot thanks brother
😀🤝

[@fatima-oy7gk]

You explain things so nicely. I don't even bother taking my calculus classes because I just can't understand my teacher.

[@tobaterja4822]

thank you so much for this great video

[@con-0310]

Love it! Thank you sir ❣

[@no_o1ne151]

I have no words to thank you 😭.

[@redaziada2181]

thank you so much this was so helpful

[@atkoamatarp8694]

Thank you for your amazing video.
I have some question.
So, in the last explanation the function is concave down on (1, 5) or (1, 5) except 4?

[@parthtiwari8413]

You are a life saver man

[@done2913]

you are saving my grade thank yu so much

[@sarimkhan9519]

Thank you so much man❤

[@kaweisimbil4678]

Thank you, it helped alot.

[@jomar1270]

Amazing job

[@FunCode123]

Thank you sir!

[@gavinp7692]

i hope these thankful comments bring u joy.... on that note I am leaving my thanks for saving me in some way, thank you for the hope for possibly passing.

[@jakodiere8207]

Bro, you have really helped me. Rolles theorem n mean value

[@RohanRajBEC]

buddy, u r great , u helped me a lot

[@lowlesssate1934]

very good teaching.

[@SuperSwagman25]

u explain so well

[@franciscafadairo8106]

Thanks and God bless you!!!!

[@bscc181]

If u were teacher from my class 11 I would have cleared jee advance easily

[@MrSilkor]

I want to thank you

[@shameemauvais4180]

Most helpfull class👍🏻

[@life_with_aida]

He just made me understand this topic in 12 mins only while my professor took 2 classes...

[@user-jo3ni7qq1m]

Thank you so much ☺️

[@mzhdaa]

thank youuuuu so muchh you are my hero 🥺😍❤️🙏

[@bromaro]

Bro thank you so much

[@vimbainashemuchuweni1010]

appreciated sir ......many thanks

[@shadyappiah99]

thanks very much..Keep on

[@nehemiacalixte3289]

you helped me through high school calc and now you’re helping me through college calc, thank YOUUUUU 😭😭😭😭😭

[@Shaz-oo8lq]

If there's a cusp at a point, and that point is between 2 concave ups, could we include the cusp in the interval of concave up for example a cusp at 0, but the interval of concave up is (-1,2)?

[@josephryan9063]

Thank you.

[@zulyc8641]

Thank you so much! Just understood concavity 10 mins before my exam.

[@leanna3802]

This is amazing

[@shaharenazchowdhury4663]

Do we have to show the numbers that we are taking to know whether that number shows Positive sign in the number of negative sign ?

[@garr6448]

easily the greatest

[@paulbornaah468]

Thanks a lot🙏🙏🙏🙏🙏

[@laibakhan8380]

Thanks. Lovee you

[@bluegrassbassing3790]

Thank you sir

[@DestructiveDj]

thank u brother

[@Janjo64]

Appreciate this omg

[@mariozanetti6069]

this guy is a good guy

[@silverluck4]

Thank you

[@throughsarahseyes4408]

I love you. Thank you!!!!!!!!

[@kitkat-xe6nc]

We love you!

[@aungkyawphyo4069]

Your videos help my life sir. You saved me for my exam

[@HabibUrRahman-sr2wn]

Now for the second example if i want to know the intervals on which graph is increasing or decreasing right from this diagram without even getting into the first derivative thing
How can i find increasing and decreasing intervals.
I saw your other video on that but that seems a bit hard...

[@Emik08_]

thank you very much^10

[@riazkhan6858]

Fantastic sir god bless you💞💗💖💕

[@asifsal7124]

@TheOrganicChemistryTutor
I am totally confused that if we can find the local and absolut Maxima and Manima with the First Derivative Test then why do we use the second Derivative test? Isn't only the first one enough? Please explain.

[@sophiaw2195]

You don't need the Second Derivative Test, but it can be a faster way of determining whether the critical points are relative maxima or minima

[@stimulus7222]

Sec derv test is for the x coord of the inflection point

[@EzzzZZZ___]

you are the G.O.A.T

[@user-bu8mg7uq3s]

thank you

[@levicletux4978]

that's good thanks

[@lanadelray9169]

A question : if we have second derivative equals zero only for x=6 for example and that is its (- 5 -) will then we say it’s convex for all real numbers or for all real numbers except 5

[@muhammad.husnain6819]

Way better than my math teacher

[@alizaman8407]

Thank u sir....................