Calculus 1 Lecture 3.4: The Second Derivative Test for Concavity of Functions

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now it's 7 years...

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Math doesn't change

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I think your teacher should give half his salary to Mr. Leonard !! The good thing about being a teacher is they get paid irrespective of how good or bad they are !! whereas any other job, you get fired if you are not good at it. Majority of teachers I have seen are horrible !! that is my experience. Then we have very very few people like Leonard who are exceptions to the rule. ! Mr. Leonard is a dream for most of math students. Thanks to you tube and thanks to Mr. Leonard's great heart which thought of recording and posting the videos. They are invaluable treasures of knowledge and great tools to have around one's knowledge belt, and save millions of students lives from destruction and hopeless existence due to those kind of teachers out there. God bless Leonard and his family !

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Got an A. Godbless Leonard.

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Same dude. I just did my first week of Calc 1 and I’m already almost done with my 6 sets of homework due over two weeks from now lol. I was literally in class doing homework for weeks ahead. I can’t wait to finish this playlist and get a sneak peek at Calc 2. Professor Leonard is the goat!

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this definitely the best explanation for this topic you will ever see

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Professor Leonard make calculus so fascinating !

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@@ckzombie1130 Merced College actually. It's the community college in a small town in the Central Valley of California.. he lives about 30 mins from me. I would love to meet him and thank him in person sometime.

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[@alenaalena9322]

Last semester, i failed our quiz, about concavity, I feel bad that I haven’t discovered these channel back then. But still, I’m grateful with this channel for preparation for my upcoming board exam in the near future.

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Love how the people who make it past 1.5, just don't stop. Great videos Prof!

[@foku9000]

Thanks! You explain this very well, unlike my current professor.

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If my professor made videos like this, no one would have a clue what on earth he is talking about. Why can't I just have this guy as my Calc professor?

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[@nint1359]

"By a show of hands, how many people feel ok with our second derivative test?" Me, hand raised, crying tears of joy.

[@warrenfranklin6173]

Professor Leonard.....thank you thank you thank you!!!!!! Oh my god, this was Way easier to follow than what I learned in class or in the textbook. You made this process so much easier to follow and I certainly understand how to do this now :) You are Awesome! I now love second derivatives! (sometimes)

[@kristinagremi4781]

Thank you so much for your help. You remind me of my high school calc teacher, my current prof isnt so good and I feel like I have to figure a lot out on my own. You help me fill in those gaps. You're the best

[@justok3702]

this explaination helped so much because i wasnt understanding the application of the second derivative rule or concavity now it makes a lot more sense

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[@TheCandyPixel]

your'e one of the people who positively influenced the life of hundreds of thousands of people, hence you are and will always be one of the good people on earth...

[@chrisweber759]

Candy Pixel lol why do you have to make it so weird

[@smoslc]

He's testing for concavity by examining the second derivative on each side of the PIPs, which is correct. But he's calling this the "Second Derivative Test", which I think is incorrect. The Second Derivative Test is defined by most textbooks to be another way of testing for maxima and minima, NOT for concavity. The second derivative tells us concavity - that is a fact, but the Second Derivative Test is not a test for concavity - with the Second Derivative Test, we plug a point into the second derivative and if the result is positive then the curve is concave up at that point, meaning that point is a relative min. If the result is negative then the curve is concave down, meaning that point is a relative max. Of course, his textbook might define the Test differently but I would be surprised if that was the case.

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[@godsmack1985]

You sir, are a saint.

[@sebastian-nunez]

That number line method is so much better than making a table...

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watching in 2022, what a lecture! thank you

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Thank you for saving my ass and helping me through my toughest subject.

[@heather0572]

Could you please turn on captions for this video?

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im here in 2024 and thanks a lot prof, cuz ur videos are super amazing, i understand better from here than from my teacher

[@parinitiverma9895]

At 21:00 , shouldn't the value of x be infinite? Because only 1/infinity is 0, not 1/0?

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Professor Leonard.thank you

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Sir plz add subtitles on all ur videos for calculus..it will be easy for us...GID bless u.

[@ammarajaz6439]

At 12:00, do you plug the numbers in 12x^2 - 24x?

[@charlesamofordjuoh9940]

will you do calculus 3?

[@Kbaf4]

he said next semester about 2 months ago, so I'm guessing he'll start sometime around now

[@jocelynarosemena3366]

Wow, thank you so much. This was such a big help.

[@sirrayr]

Sir as per definition Inflextion point {NOTE -it is a point so i must have (x,y) value}:-is that point when concavity changes its sign from positive to negative (or vice versa) Pls tell me then in case of vertical asymtote at what point the inflection point exist( i mean ihave x cordinate valve ( for eg- 1/x asymtote exist at x=0) but i cant figure out tha value for y condinade.. for inflection point..???????????? Pls help me i cant find this answere on internet

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Oh my gosh, this is so cool!!

[@elgozk]

So many students having to watch this to explain what their professors couldn't. The professors need to watch so they can learn how to properly demonstrate mathematical concepts.

[@ctamai]

For the last example at 34:50, did anyone else get REL MAX (-2,-4), REL MIN (4,-112), and IP (1,-58)? I plugged the x-values into the OG function.

[@abeerkhurram6389]

I got the same, I'm tryna figure how they got those values

[@dazddragon3692]

the conjuirng guy o_o ....good teacher

[@bleach7721]

Thankyou

[@mrinalthakur3946]

sir what do we do for functions with discontinuity or a function like sinx where x=infinty

[@kevin4675]

I think something wrong. The denominator can't be 0. at 21:11

[@lesliedapple390]

really cool!

[@brianacorrielus8890]

Thank you

[@michaelprozonic]

I had Calculus 1 over fifty years ago and this was never explained this clearly. Also, my lecture had over 300 students in it given in an auditorium with only chalkboards and no microphones. No professor / student interaction and no questions from students allowed

[@ahmedalanbagi1416]

i pay 2k to learn a class in college just to learn from youtube

[@danielbaker2449]

@josephramirez I had the same issue and was about to lose my mind until I realize that I misread the professors problem as -32 at the end instead of a +32. Once I realized it was a +32, I found the numbers no problem. Hopefully nobody else wastes as much time as I did! haha

[@michaelzanfardino5931]

haha wheres the graph for comments... ive been watching literally every video since algebra almost at calc 2 wooo... each comment section is just praising the hero we all needed... doc leo master manipulator of the majestical mathematics... super powers: controls the curvature of spacetime allowing him to play with the strings of all 11 dimensions... weakness: the pause button.... a button that has been lost for millennia last saw in a universe far far away... if found has the power to pause the video and the world cannot learn the truth therefore the end of existence as we know it

[@MashallahHafiz]

Professor, by any chance would you know the name of the video where you cover Anti derivatives?

[@chrisweber759]

Mohammed Siddiqui dude look it up the guy isn't gonna take time out of his busy day to answer a question you can figure out yourself

[@jaxonstuart7132]

Having a hard time finding a video on finding derivative of logs. Do you have one that I’m not seeing?

[@ZaneleMtsweni-bc3tg]

DID YOU FIND IT?

[@nikitakain6217]

could you just please explain why X=0 is not certainly an inflection point and also please explain why the table is made downward for 2nd derivative sign check

[@Davidn1]

X^4 is always concave up, yet at x=0, f''(x) touches zero. That's why you check to see if the second derivative changes sign across the possible inflection point.

[@maxaltamimi1901]

great job sir, thank you !

[@cennemidiaz7903]

gasp* ...... I understand. thank uuuuuuu

[@oliverdacracker]

This man put me through highschool and now university lol

[@Jasonasked1233]

When I found the R. Max, it gave me 84, not 60. Did anyone else get that?

[@awakenonline5098]

I feel bad because no one replied you in time I know I am super late but still... I will answer your question No brother, the value of R. Max is not 84 (Kindly double check your calculations, I am pretty sure that it's 60)

[@Jasonasked1233]

@@awakenonline5098 I'm relearning this all over again, Wow 3 years have passed, Thank you!

[@amorozzo19]

Thanks so much for your videos. I have benefited a lot from them. FYI: At 35:37, the answer is (-2, 4), (4, -112), and (1, -58). Did anyone else get these answers?

[@egoiisticprince7977]

yes u r right

[@spooderman5405]

No, the function is x^3-3x^2-24x+32 It almost looks -32 at the end of the function what he wrote .

[@chrisschmitt4380]

These are correct. You can graph it and verify this

[@homerthompson7427]

At 14:24, I think the dolphin was asking you a question.

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I love you

[@mehrpouyamovahadi1542]

3:24 "Testuh" hard to write it in words lol

[@ruandersongabriel1385]

Just me that raise the hand too, even knowing he won't see it ? Hahahahha

[@wnooristany539]

for 22:16 how can x=-1 be a 0 when its undefined? should there just be no inflection point because there is no x value that will be 0?

[@LunarPegasus75]

W Nooristany you prob already know this but critical points include -where a derivative is equal to 0 -endpts -where the derivative does not exist or in other words makes the function undefined (which in this case was x =1)

[@fibblasnubbla9105]

Yes! I agree. This time the professor seems to have made a serious error. Not often but it happens. You cannot divide by zero as he just did finding the point x = 1 where f''(x) is 0. f''(x) is not 0 at x=1 - on the contrary, it approaches the assymptote x=1 infinitely. The funktion f(x) does in fact have an inflection point at x=1 but it does so in a strange way, notably in the sense that f'(x) ie the first derivative or slope of main function increases indefinitely as x approaches 1 (in order to have slope = "infinity"). x = 1 is a critical point vs 1st derivative in sense it is't defined at all. I am surprised no one in the class reacted....:) Apart from that I think this is a fabulous series.... Love

[@aaqibmehraj4339]

@@fibblasnubbla9105 i m too thinking about ths right now

[@ptyxs]

This point (1, 0) [Nota bene : not -1, 0] is undefined for derivative functions (first derivative g', second derivative g'' and so on), but it is perfectly defined for the original function g. g has no derivative at this point (because its slope is vertical).

[@User-fm3tv]

Why are more people not like this calc. God?

[@blainevanity6]

Thank you T_T

[@ThatOneScienceGuy]

At 18:38 someone says -5/6. Wtf? Lol.

[@awakenonline5098]

Someone was doin' *METH* instead of *MATH*

[@gildeshokka7721]

Mr. Valentino did it better!

[@dashaagafonova519]

4:16 "третья в строке"?

[@adrianloh6919]

Don’t use your pen to knock your teeth. I hate that sound.....

[@prushahunar160]

is it just me who thinks he's so hot and couldn't concentrate

[@laurenbarbee727]

that +32 is AWFUL hard to see..