Second Derivative Test

This calculus video tutorial provides a basic introduction into the second derivative test. It explains how to use the second derivative test to identify the presence of a relative maximum or a relative minimum at a critical point. If the second derivative is positive at a critical number - a local minimum is present. If the second derivative is negative at a critical number - a local maximum is present. So to identify the relative extrema, find the first derivative, set it equal to zero and identify the critical numbers. Plug the critical numbers into the second derivative function to determine the concavity of the function to see if its concave up or concave down. If it's concave up - it's a relative maximum. If it's concave down, it's a relative minimum. You can confirm the results of the second derivative test using the first derivative test with a sign chart on a number line.
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/Gh48aOvWcxw/video.html
Final Exams and Video Playlists: www.video-tutor.net/

[@mrfatboy327]

The problem for me is that I get bored during classes and tend to zone out constantly. These videos are quick and to the point, a sort of TLDR which really helps me with my limited attention span.

[@jeanrenzocaldito4688]

Feel you bro... I did feel myself on your ground, during class you say? 😁

[@jamien.5528]

SAME. I have no idea if I have adhd or not

[@undercoverelle]

literally same i started doing online these past two weeks and i havent learned anything and i have my final friday so now im trying to teach myself the last unit

[@Steve-sz4bh]

@@jamien.5528 You probably do. This is precisely how I was, so I spoke to a psychiatrist and was diagnosed with ADHD. I first tried Ritalin, and It wasn't working for me, but I was young and dumb, so I kept saying it was because I felt it was the only option. Then I finally tried Adderall, and my grades increased, and I started to focus and retain all of the knowledge that was conveyed in my classes. It has significantly improved my life for the better, and I recommend speaking with a psychiatrist asap.

[@RICHFRVR]

Try putting your phone to the side.

[@leahc3846]

Currently in my fifth and hopefully final semester of college. I just wanted to take second to thank the organic chemistry tutor for getting me this far. Couldn't have done it without you

[@manavgupta2059]

Bruh ya in college and u don't know this? Is ur country's college education so bad?

[@alexcoutinho1128]

These videos are so useful
I’ve learned more from your videos than my calculus teacher

[@viragkatai_urban6790]

Same bro

[@nathanclements787]

@@viragkatai_urban6790 my teachers handwriting is unreadable..

[@gregcandy8900]

The hero we need but dont deserve

[@KaletheQuick]

I listened to this on the way to my calc CLEP test. One question on there was this stuff exactly, and I remembered this vid.
I passed by one point.
Thank you so much for all the great videos! I've been watching them for years trying to pass calc 1! And now I have. Thank you so much!😊

[@kaiyabou]

Final in half an hour. Thanks for everything man! 😔✊🏽

[@kaiyabou]

Katlo Oleteng passed the class thankfully.

[@amintimani6034]

final in 5 hours :D

[@pranaymohla3965]

lol same midterms in half

[@ruairiwalsh5314]

@@kaiyabou bit late but well done

[@GSDKXV]

This generation is so lucky

[@brianbc4]

I'm currently taking calculus for the summer and my grade depends on you

[@superlife9307]

What happened with your grades

[@brianbc4]

@@superlife9307 I passed it with 87%

[@FavouredElm2]

@@brianbc4 congratulations man.... I have my exams.. Let's see how it goes

[@brianbc4]

@@FavouredElm2Wish you all the best!

[@Omar-ic3wc]

Great job!! My compliments man

[@julissaarias341]

Thanks so much for all these videos, im taking calculus 1 and physics 1 and your channel is my go to for homework help and to study for exam, so far i have done really well, so thank you again :)

[@AyeItsFon]

this dude needs to do a face reveal

[@etmaille]

Forreal

[@rabi0246]

why tho

[@AyeItsFon]

a random guy why not?

[@FirstLast-ws7zw]

@@AyeItsFon You don't have to see his face to understand his content

[@Fatma-id1vq]

Indeed

[@jiskoboutv7460]

this guy is a Pro.. I hope that you have a nice job ,,,,,,, cause you are really brillant... you explain everything calm and right
thanks a lot man........

[@angelam5649]

I have a test on this stuff and you are a life saver honestly

[@asifsal7124]

So why did I start to first hit the "Like" then start watching the video?
You are the Genius.

[@divyanshiupadhyay513]

We all wonder...I did the same😭

[@menabrook3214]

Thank you soooooooooo sooooooooo much for these videos. They are extremely helpful and ive been able to understand the concepts and topics more. The way you teach is so organized and neat I am able to stay focused and I actually engage with the examples you do and do it on my own and then fact check.

[@idaho9479]

Clear, concise, to the point- thank you!

[@gracedouglas6031]

You are absolutely amazing!!! Thank you for such short but effective videos. You manage to teach me in 13 minutes what my teacher couldn't convey in a week of class!!

[@ian.ambrose]

That's bad lol. Wasting people's time (in this case, the teacher wasting your time) is basically a crime. It's a crime for the education system to pick bad teachers. I don't attend any math class but watching these videos in 2 days helped me theoretically mastered max & min, just a few more practices and I will be good. Basically I saved a whole week compared to you.

[@antoniolomeli7956]

@@ian.ambrose They can’t really “save a week” of time though since they’re obligated to go to class anyway lol

[@ian.ambrose]

@@antoniolomeli7956 Yeah makes sense.

[@ayshaghanawi9941]

You have no idea how many people you've helped with your videos. You are truly a blessing from God! God bless you :'D

[@ryankeshet5820]

You are such a good teacher and helper. I subbed.

[@intisher9363]

you are the reason i am still chill while tomorrow is my mid.love you .carry on

[@mwalsh5542]

I help my daughter with math and your videos help tremendously. Thank you.

[@manavgupta2059]

No smack like, crush subscribe, unprotected share but only pure education ❤❤
Well done

[@sids9551]

This guy is a life saver for my calc class right now

[@marco3391]

bro has a video on everything, legend

[@djs9931]

Thanks man, really helped.

[@emiliashaw6909]

These videos have helped me get As in high school Chem 11/12, Pre calc 11/12, Calc 12, physics 12 and now uni calc 1 and physics 1

[@ahmedzuhair4355]

Thank you sir it was very much helpful for me. I was troubling with this topic.

[@done2913]

you are one of the greatest teacher. thank you so much it helps me alot

[@kentenfaust3042]

I watch these before all of my calculus tests, and trust me, he’s the only reason I’m passing.😂😂
Thank you very much!

[@Thpeakingfactth]

This man be doing so much good in the world

[@tanushrih2178]

I've said this once, I'll say it again, this dude is a life saver ✋

[@sicilianotoronto]

Thank you for calming my nerves and saving me hours of wasted study time!

[@jakapockaj2034]

great video, simply explained👍

[@tinyade.s]

Yes this video helped!! Thank you

[@ChrisJunio.211]

Thanks alot you made me understand well well

[@jamien.5528]

Thank you so much your videos make math so easy to understand

[@deidei2305]

Great vid and explanation

[@ashanbutt3978]

You are a blessing ...! May God bless you🌠

[@quinnjones2886]

Can you do some examples with trig functions? Use the second derivative test to find local extrema of a sine or cosine function
?

[@alessandrolagi2147]

THANK YOU SO MUCH!!

[@widerule1686]

I paid $400 for the calculus class im taking now. you deserve that money more than the school does.

[@ian.ambrose]

He has a Patreon that I'm sure has more hardcore contents up there. It sure is more beneficial buying his classes than any other classes out there.

[@trishsithole122]

you are the bomb!!! thank you so much

[@sarashaikh2018]

Thank you so much sir.. It helps me lot

[@mnmvideos4352]

Helping me not fail first year engineering calc!

[@jeanrenzocaldito4688]

Uhhhmmm... Just wanted to support you bro. Let's hang up our BEGGING banner, will ye? 😂🤣

[@gokul_2810]

Thankssss a lotttt mann 🥺❤

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for showing students/nonstudents How to use /apply the Second Derivative Test to find Relative Maximum/Minimum at a critical point in Calculus. This is an error free video/lecture on CZcams TV with the Organic Chemistry Tutor.

[@redshahstar]

Best tutor in the world

[@vicc.4290]

Thank you sir.

[@imnobody101]

To find the actual point of the extrema, would we plug our x value that we got from the second derivative test back into the first function?

[@ts37924]

is the change in slope (i.e the second derevitive) of a * maxima * or a * minima * must always be * negetive dec. * or
* positive inc. * respectively or can it be * zero * at any of them aswell?

[@donnearendse5645]

Thank you🙏🏽

[@daoudhussain979]

Your channel name should have been CALCULAS TEACHER. Great content man!

[@napkinshoplifta5163]

Love this guy

[@GoScience123]

Bro I feel like I'm being taught math by Mark Wahlberg lmao

[@VasHappenin7107]

GOD YES

[@JrMoreno88]

Makes math that much extreme. Like I'm trying to hack something

[@hisyamhasbi8257]

Who's that guys

[@metawhirl4609]

That's lame

[@Brian-ou7bl]

thank you

[@Matt-sg1kx]

Nice explanation

[@yeshuevsr4452]

Gr8 work

[@noellemichaelabalbuena8127]

Thank you Sir.

[@Himawari_.]

thank you soo much

[@chrismartin1993]

Trying to find the inflection point of an equation of curve. y=5.075e^(.2136x). equation goes from positive to negative. I have a lot of these to do so would like an online calculator. Can you point me in right direction. Did I give you enough information ?

[@speconcloud9]

This GUY Deserver Respect and LUV 110%

[@janieli]

at 1:37, if f’(c) = 0 and f’’(c) is just the slope of the derivative at x value of c. why isnt f’’(c) just equal to 0?

[@dougallan9514]

So what is the benefit of using the second derivative test vs the first..?

[@beartheburn3863]

After putting the critical values in the second derivative if f"(c) = 0 then we go back to first derivative test ...
Actually both tests are used but it depends on you which one to use ....
Well I would say learn both the tests because you could be asked to apply any one of them
Hope this helps...

[@ishaperry8878]

you are amazing

[@yagzyalcntas553]

I am at 1:08 and already had all my answers thank you :D

[@sb19dugyot63]

What if there is the same sign in critical number?

[@sewind6613]

I understand the calculations. What I don't understand is why, when I graph the equation in Geobegra, that a turning point appears to be (-3, -26) and not (-2,-15). Anyone can help me to understand? Thank you.

[@noranmohamed2867]

Thank you

[@ozymandias1389]

Why is the 2nd derivative negative with a relative maximum and positive with a relative minimum, and what happens if the 2nd derivative is 0

[@mohammadismailhossain6435]

2nd derivative -ve → concave down→relative maximum
2nd derivative +ve → concave up → relative minimum
👌

[@jameow4890]

Thanks

[@arjansingh8289]

What if f'(c) = f''(c)? Would that mean that there are no relative extrema?

[@c1kada873]

what if the 2nd derivative is a constant?

[@sllanguageschool147]

If we can easily find using 1st derivative test, why we need second derivative as well?

[@uditsaxena3844]

thanks alot

[@Silver-wt3fj]

This stuff just doesn't register when im in class, thanks for the to the point explanation

[@TheWizard856]

I love how your advertisements are made redundant by your excellent Math tutoring skills. LOL!

[@ArunKumar-yb2jn]

But how this connected with the main function? Explanation is not clear on that part.

[@abdullahawan6224]

What to do incase if double derivative gives 0 at critical points.

[@subratprasadnayak6195]

Thanks you so much...

[@yahyaekin8072]

Every hero does not wear cloak, thanks a lot.

[@czarinc.6971]

ok but how would you do it with a rational???

[@nadineruiz5859]

MY TEACHER DID NOT TEACH ME ANYYY OF THIS. THANK YOU!

[@annieqian7590]

[@wafa_sh_hds1]

سپاست مامۆستای بەڕێز

[@Alphae21]

goat?

[@vaiebhavpatil2340]

He: now it's ur turn
Me: YASS😎

[@PHILLYMEDIC69]

so you can only do this if you have critical numbers?

[@sunny.b4213]

yessir

[@davidm3210]

The first derivative test for extrema, and the second derivative for inflection points seems more intuitive to me.

[@beartheburn3863]

Yup

[@ian.ambrose]

That's very cool.

[@mahmoudnadi1992]

Watching this 30 min before my midterm 😂😭😱

[@beartheburn3863]

Watching 2 days before my finals ....

[@arinalexus7556]

Watching the day before

[@azaa2188]

1. Find critical numbers (F'=0)
2. Find out scond derivative (F'') at those critical points

[@PHILLYMEDIC69]

i bet this guy can score 100 on an mcat...

[@user-fn4ds7zm1i]

Highest score on mcat is 528.

[@josh1234567892]

Z_Boss_23 so then he probably could score a 100

[@shahsifat3220]

My classmates failed after attending all classes.I with just watching 8 videos from this channel Top the class with zero Attendence

[@fatusopp4739]

thx bbg

[@sumantapanigrahi3765]

You just save me

[@autointake3679]

For you're last example, when 12x^2-12x-24=0, are the roots not x=2 and -1 (instead of -2 and 1) as putting your values in you dont get 0 and my calculator said my x values were correct? Great vid tho helped alot👍🏽

[@booktalk8205]

I’m pisssed that I’ve been doing this the harder way

[@CourageKubi]

I'm sure we are plenty here watching 5yrs ago video 😊

[@redgefleming1535]

Is it possible to get 3 critical points and 2 inflection points?

[@jamaiya7]

redge fleming yes!

[@tortillajoe9942]

Any function can have any number of either.

[@dhanma3953]

Can someone explain to me how 4x cube become 12x squared and 6xsquared become negative 12x i really suck at math

[@JKMath]

He was using the power rule for derivatives. You may want to look up a separate video to learn that topic first before continuing (you can look for one of his videos, or you can check out mine which I will have linked at the end of this comment). But for the example in this video that you are referring to, the derivative of 4x^3 is done as follows: Multiply the function by the exponent, 3, and then subtract one from the exponent. So you will have 3*4x^(3-1) which then is equal to 12x^2 if you simplify it. The same thing would happen for 6x^2. Hope this helps, and here is the link to the video I mentioned earlier: czcams.com/video/izMX5wx7ZlQ/video.html

[@Cristian-ie9et]

I guess it’s a massage into mental math... I can visualize quadratic fn. on all quadrants unless I forget

[@mosup5007]

I was looking for the reason why