❖ Concavity, Inflection Points and Second Derivatives ❖

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  • Опубліковано 18 гру 2024

КОМЕНТАРІ • 452

  • @patrickjmt
    @patrickjmt  15 років тому +59

    first derivative is used to find increasing/decreasing local max/mins
    second derivative can be used to find concavity and local max/mins (usually)

    • @MUNIR_FF011
      @MUNIR_FF011 Рік тому

      where is point of inflection

    • @potchi7340
      @potchi7340 8 місяців тому

      ​@@MUNIR_FF011concavity

  • @coolkidyo9
    @coolkidyo9 9 років тому +191

    Concave up like a cup
    Concave down like a frown
    Let's see how I do on this final tomorrow :)

  • @stephanelombardo
    @stephanelombardo 10 років тому +38

    Patrick, I have to thank you for the clear math tutorial you are offering online via youtube. I am a student in one of the colleges in Ontario, Canada and just enjoy watching your math and calculus problems with your fascinating explanation. So clear, that I get it right after watching one or two times about a problem I have!
    I thank you for everything you do to your community and others by taking time, video recording these math problem solving.
    Sam

    • @JohnCena-mu3lv
      @JohnCena-mu3lv 10 років тому +1

      Stephane Lombardo tag him if you want to ensure that he will read your comment

  • @Godot8
    @Godot8 10 років тому +106

    Haven't gone to math class the entire unit. Test tomorrow at 10:30, haven't learned a thing due to my laziness. However, thanks to aderol, an all nighter, and patrickJMT, I may be able to ace this fucker. You're a fuckin' bro JMT, a fuckin' bro.

    • @PassTheMusik
      @PassTheMusik 10 років тому +18

      lmao this is me right now, never gonna miss class again, even though my teacher sucks dick.

    • @Punjabispitta
      @Punjabispitta 10 років тому

      haha this was me 4 weeks ago too! lmfao

    • @zjuan8
      @zjuan8 10 років тому

      Harnoor Singh this is me now lmao

    • @Punjabispitta
      @Punjabispitta 10 років тому +1

      zjuan8 lol yeah me too, after I posted that comment, I was like, "Wait, I need to know this for finals, don't I.." The past always comes back to haunt you, I swear -__-

    • @Samynumberone
      @Samynumberone 9 років тому

      Jonathan Nieder this is me right now

  • @griffinpheto2324
    @griffinpheto2324 5 років тому +5

    You've just explained in 10 minutes what my lecturer couldn't explain all semester...THANK YOU

  • @Isteshhad
    @Isteshhad 12 років тому

    I swear, you are the best tutor in the world. Not even exaggerating over here !!!! May God continue to bless you and increase you in knowledge,

  • @CausticTitan
    @CausticTitan 6 років тому

    Your explanations are much better than anyone else's on UA-cam. You put the math into plain English; I appreciate your explanations.

  • @darleneL023
    @darleneL023 11 років тому +27

    Thank you! I've been looking at Khan Academy because all the comments say it's so great and was staring at his videos like an idiot. You clear everything up!

    • @beriakasongu2492
      @beriakasongu2492 6 років тому +5

      i thought i was the only one who failed to follow khan academy

  • @jjeon9850
    @jjeon9850 9 років тому +96

    9:18- "yuck" - made me laugh so hard

  • @espy7
    @espy7 6 років тому +1

    i'm studying for my EIT (engineer in training) exam, saw your video on the side and the memories came rushing back. made me happy. I had to stop by and show some love.

  • @bryantp64
    @bryantp64 6 років тому +35

    During first example: “oh okay, it looks simple”
    Second example: “wtf....”

  • @patrickjmt
    @patrickjmt  16 років тому +1

    once you have it factored, you set each part equal to zero. since 6 can not equal zero, we just leave it out.
    and for the factoring part: i use the difference of perfect squares formula:
    x^2 - y^2 = (x + y)(x - y)
    so to factor x^2-1, use
    x^2 - 1= (x + 1)(x - 1)
    and the same thing on the 5x^2-1 part!

  • @jimmysuszynski3010
    @jimmysuszynski3010 10 років тому +147

    the car alarm was killin' me lol great vid tho very explanatory

    • @ijkauvaka5212
      @ijkauvaka5212 9 років тому +3

      Seriously I thought it was just me! But, yeah, still helpful.

    • @morgangregory5528
      @morgangregory5528 6 років тому

      it sounds like a hospital monitor....i think he might be in a hospital

  • @nacal9550
    @nacal9550 9 років тому +89

    i love you man, when i graduate, im going to buy you a bottle. #truuuuuu

    • @patrickjmt
      @patrickjmt  9 років тому +36

      +Kevin Carrasco will there be anything any it?

    • @nacal9550
      @nacal9550 9 років тому +18

      +patrickJMT just a receipt if you want to return it. Thank you for your work.

    • @vonaxl7617
      @vonaxl7617 9 років тому +31

      +Kevin Carrasco Hahahaha I second this.
      I'll even throw a speech for you when I do my walk to pick up my diploma. "I could not have done without w/o +PatrickJMT"

    • @xhsxspectre
      @xhsxspectre 6 років тому +2

      @dark he didnt

    • @kristianbusby1895
      @kristianbusby1895 6 років тому

      same, IF I graduate...

  • @noseasmamut
    @noseasmamut 13 років тому

    Patrick thank you so much for your contributions to the world. You have decreased the number of headaches caused by calculus. Again thank you.

  • @celestinestoltenberg8177
    @celestinestoltenberg8177 12 років тому

    You are a lifesaver! I am currently enrolled in an online calculus class and there is NO lecture. I just can't get these concepts without seeing and hearing someone explain it. I've lots watched of videos, and yours are some of the best. I'm telling the rest of my class about you. :)

  • @DudeMr94
    @DudeMr94 10 років тому

    Dude, I love your explanations... its so much clearer than my teacher!!! And I love that your voice is not freakin monotonous.

  • @edwinberduo6146
    @edwinberduo6146 5 років тому

    I am watching this video 11 years after you posted this, and it still helps

  • @sarahmann6716
    @sarahmann6716 6 років тому

    I loved PatrickJMT when I was taking calc four years ago and I still love him today as I am tutoring and he makes great refreshers. Thank you PatrickJMT!

  • @jagdeepshoker
    @jagdeepshoker 12 років тому

    The fire alarm was going off in the background but Patrick disregarded it and put his life on the line in order to save math kids around the world from failing. A real hero .
    :)

  • @midnull
    @midnull 11 років тому +2

    Thank you so much sir!!!!! This is a far better explanation then most of the teachers/tutors that I've had!

  • @finestbravest
    @finestbravest 14 років тому

    Patrick you are by far the best instructor... Thank you for taking the time to do this service. MUAH!!!

  • @lilythatgirl
    @lilythatgirl 13 років тому

    I just wanted to thank you so very much for the amazingly easy to understand videos which you have posted all throughout UA-cam. I got a 97 in calc b/c of you PatrickJMT!! Keep it up! :)

  • @patrickjmt
    @patrickjmt  12 років тому +2

    if at a point, the function changes concavity, it is an inflection point

  • @Ccsher
    @Ccsher 9 років тому +38

    i'm very sleep deprived rn and the car alarm fucked me up.... kept pausing the video and stopped hearing it and definitely thought i was crazy ahahah

  • @SuperBunbun14
    @SuperBunbun14 8 років тому +1

    Honestly, I can't thank you enough. You've explained it so clearly!

  • @konichiwasupersan
    @konichiwasupersan 13 років тому

    These videos are the only way I am passing Calculus! Thnx so much!

  • @HeyWheresKel
    @HeyWheresKel 16 років тому

    man, your videos are so helpful....
    i seriously need to refer to them more often.

  • @patrickjmt
    @patrickjmt  12 років тому +1

    happy to help :) just think of patrickjmt talking to you when you take your final!

  • @nickstory
    @nickstory 12 років тому

    holy shit i have a midterm in 5 days, and this is the most useful channel ever. wheres the donation button

  • @MyJuicehole
    @MyJuicehole 12 років тому

    Can't wait to stomp on my final tomorrow. I've done all your example problems so far and I have done everything correctly. I'm ready

  • @skrevat
    @skrevat 14 років тому

    Just wanted to say-- My math department steals problems from MIT, and this is the exact first example they had me doing in my homework. No coincidence- you're a great teacher!

  • @imapiratedammit
    @imapiratedammit 12 років тому

    i like how these videos can cover almost a whole semester in about an hour

  • @CuteyAndy
    @CuteyAndy 12 років тому

    Someone give this man a diamond medal.

  • @that_danishdude
    @that_danishdude 12 років тому

    Thank you so much. My math professor is impossible to understand, and you somehow make everything clear and easy!

  • @KrisSavvys
    @KrisSavvys 14 років тому

    all your vids are helping me alot for my upcoming tests and my midterm next week haha. very much appreciated man

  • @2manameturfilms13
    @2manameturfilms13 12 років тому

    Here is my day...
    Go to calculus class and become confused.
    Go home and get on this channel
    Find exactly what my teacher was trying to explain on said channel
    Finally understand!!!

  • @ShaanNotShawn
    @ShaanNotShawn 15 років тому

    thank you so much! i learned a week of calculus within 30 minutes thanks to your videos!

  • @snoopylover8
    @snoopylover8 13 років тому

    Dear Patrick,
    Thank you so much for uploading all of these videos! I know this is bad, but I occasionally I fall asleep in my AP Calculus AB class and miss parts of the lesson. Your videos are PERFECT for filling in my mental holes. I really think UA-cam should give you an award or something for your contributions. :)
    PS i love your handwriting.

  • @TRUNKER76
    @TRUNKER76 15 років тому

    yep I've had the exact same experience. Luckily we have Patrick here to help us with our algebra too!

  • @AliJanjua
    @AliJanjua 15 років тому

    dude this is excellent. I am doing calculus after seven years and now using it in my masters and your videos especially this one helped me alot.

  • @casanovabloop
    @casanovabloop 11 років тому

    This is so understandable and makes what was a foreign language to me very simple.

  • @TNTMADNESS
    @TNTMADNESS 6 років тому

    Most helpful guy to get you through engineering.

  • @alexh.4514
    @alexh.4514 Рік тому

    15 years later and still incredibly helpful 🙂

  • @bman9469
    @bman9469 6 років тому

    A simple video like this can make such a difference. Thanks

  • @livingliferight502
    @livingliferight502 11 років тому

    AP Calculus Exam is coming up. Reviewing with your videos makes me really confident!

  • @ArticruciA
    @ArticruciA 12 років тому

    I am reviewing for my calc final using your vids. You are awesome, and I'm hiring you as my free internet math tutor. You are awesome!

  • @sibsbubbles
    @sibsbubbles 12 років тому

    Patrick, you rule!! Wish I could replace my Calc I teacher for you instead. You get way more done way faster and explain so much better. Probably gonna be destined to re-taking Calc, but you've "got my back" so to speak.

  • @karld1571
    @karld1571 9 років тому

    You teach me more than my actual Calc teacher, good work m8

  • @austifornia
    @austifornia 7 років тому

    Yes, you are correct with everything you did in that 2nd problem you did. 1 divided by the square root of 5 is about .447 or .45 depending on how you want to round it up. Between the numbers 1 and the fraction problem with the square root sign, no matter what number between those numbers you plug back into the 2nd derivative is going to be negative either way. And you know, what else is unique about this problem is that this problem is showing that the concavity keeps flipping up and down. It's very wavy when you graph it.

  • @tiasmith1809
    @tiasmith1809 8 років тому +8

    Thanks bae. You helped me with my final

  • @staind2523
    @staind2523 15 років тому

    My calculus book...is terrible at giving clear examples (Some are good but are either too easy or are exceptions to the normal problems)...so thank you very much for your examples. Makes the whole process a lot easier.
    I can't imagine how many test scores you have single handedly improved solely because of these videos.

  • @209twitch
    @209twitch 11 років тому +1

    The 2nd derivative is just the derivative of the 1st derivative.
    Ex: F(x) = X^2 + 3x
    1st derivative: F'(x) = 2x + 3
    2nd derivative: F''(x) = 2
    Hope that helps!

  • @patrickjmt
    @patrickjmt  16 років тому

    at what time in the video?
    i could have made a mistake!

  • @shilpamathews972
    @shilpamathews972 12 років тому

    you are the reason i am passing math! thank you!!

  • @deena691D
    @deena691D 8 років тому

    words can't describe my love and appreciation, thank you man!!

  • @_KRVS
    @_KRVS 13 років тому

    Thanks for the help! You got me through my last unit exam and hopefully the next!

  • @SmokeySDA
    @SmokeySDA 15 років тому

    If it wasn't for your videos, I wouldn't have passed precal 1 & 2 and calc 1. Thank you so much!!!11

  • @Tunechi65
    @Tunechi65 11 років тому +58

    that damn car alarm driving me NUTS

    • @gilbert5646
      @gilbert5646 11 років тому +1

      ends @ 3:34 haha

    • @matthkang
      @matthkang 11 років тому +4

      gilbert5646 i still hear it ringing in my ears

  • @kickflipindy78
    @kickflipindy78 10 років тому +9

    are you in the hatch from Lost?

  • @jennaXhye818
    @jennaXhye818 12 років тому

    makes me so happy when i understand this stuff! ahah. i use your vids every day for calc & feel like i should thank you in every vid i use! so thanks :)

  • @lomgandsomejelCO
    @lomgandsomejelCO 13 років тому

    if i do well at all on my calc final, it will be one hundred percent be because of your videos. thanks!

  • @Distancerun6
    @Distancerun6 12 років тому

    You are a bold man doing calculus in a sharpie.

  • @Stinglikeabee625
    @Stinglikeabee625 14 років тому

    thx! now I'm pretty confident about my calc test tomorrow! :)

  • @BJMcB92
    @BJMcB92 11 років тому

    can you please be my calculus professor? your 10 minute videos are more helpful than my calc prof's hour long lectures

  • @honey123401
    @honey123401 12 років тому

    OMG you were in my dream last night.. I guess I watched too many of ur Maths Tutorials yesterday..

  • @mrandyinf
    @mrandyinf 12 років тому

    thanks sir
    you`re awesome, i refer all my friends to your website and they like it so much.

  • @medmuse_
    @medmuse_ 11 років тому

    The day before my AP Calculus BC Exam = A study date with PatrickJMT

  • @patrickjmt
    @patrickjmt  14 років тому

    @TheAlbania91 i sometimes turn on about 20 different random videos of mine at the same time and listen to them

  • @patrickjmt
    @patrickjmt  12 років тому

    @LARSI0N well, that was an old rule i had at the time. now i can post things that are as long as i want :)

  • @ILoveStemi
    @ILoveStemi 11 років тому +45

    I swear, no matter how many times I watch this I can never understand it. Maybe I shouldn't be in AP Calculus lol

  • @yohuallin
    @yohuallin 12 років тому

    wait, this is my professor was trying to say.... wish i had seen this channel mid semester. thanks

  • @iNewbieNick
    @iNewbieNick 9 років тому

    I thought it was hilarious how I could hear a saw and a car horn going off at the same time in the background. I don't know why I found it funny. I have an exam next week and a final in 6 weeks, thank you Patrick.

  • @Dark_Knightro
    @Dark_Knightro 4 роки тому +1

    ah! the days where youtube had a time limit on videos... I surely remember these

  • @thekaiser403
    @thekaiser403 12 років тому

    I had to work all day and i have a calc final in the morning and youre saving my ass right now

  • @wright22742
    @wright22742 12 років тому +1

    My life depends on my calculus final next Tuesday. I wish I had found your videos sooner; there is still hope though!

  • @patrickjmt
    @patrickjmt  14 років тому

    @JIAQIR hahah please, everyone : )
    thanks for the compliment

  • @Umairshahid2330
    @Umairshahid2330 12 років тому

    first one was critical points , which is used to check whether the function is decreasing or increasing and this one is inflection point .Inflection point is where the concavity of f(x) changes (goes from conave up to concave down, vice versa).

  • @kelxo1023
    @kelxo1023 11 років тому

    Saw this in class, good job

  • @roisinlee6282
    @roisinlee6282 7 років тому

    hey there! thanks for the videos, I was just wondering if anyone could explain to be what happened at 6:11 thank you!

  • @1fastcubesolver
    @1fastcubesolver 12 років тому

    You have really helped me out so much! Thank you so much for making these videos!

  • @patrickjmt
    @patrickjmt  16 років тому

    yes! absolutely correct

  • @chadpalaad8674
    @chadpalaad8674 10 років тому

    i am now ready for the AP test. thank you good sir

  • @susanhong99
    @susanhong99 13 років тому

    u can really make these problems sound so easy!! :)

  • @Poptartsforlife123
    @Poptartsforlife123 10 років тому

    Man you the real MVP!!! Thank you!!!!

  • @user-un5lt3ny7j
    @user-un5lt3ny7j 10 років тому +9

    why can't you just write my maths textbook? i wasted so much money buying it. Thanks a lot Patrick!

    • @cameronaminian9442
      @cameronaminian9442 10 років тому +5

      He has a Calculus book that you can buy. Definitely worth the money

    • @debbietan114
      @debbietan114 9 років тому

      I know right

    • @SyncStep
      @SyncStep 9 років тому

      +Cameron Aminian wait what? is this for real??

  • @lenkab123
    @lenkab123 11 років тому +1

    THIS WAS SO HELPFUL THANK YOU

  • @fevenayana6931
    @fevenayana6931 10 років тому

    Thanks man, you're a lifesaver.

  • @MrManlymanerson
    @MrManlymanerson 12 років тому

    Thank you so much. I wish I could understand my calc teacher. His accent is just so thick.

  • @Suayyyv
    @Suayyyv 7 років тому

    thankyou a hundred times so so so much cause i was about to give up and take an L on my 100pt test tmrw but now i understand:)

  • @zoom2121
    @zoom2121 14 років тому

    Do you have any videos which show how to find inflections points?
    BTW your videos seriously helped me a lot in CALC 1

  • @deathcommand
    @deathcommand 13 років тому

    Off to my math final. Hope I do well!
    Thank you as well!

  • @noturchannel6882
    @noturchannel6882 6 років тому

    Well I watched this 12 times along with some of your other videos, gonna kill the exam tomorrow♥️

  • @patrickjmt
    @patrickjmt  13 років тому

    @iloveBeaver1 glad you like my stuff : )

  • @maxaug88
    @maxaug88 9 років тому

    What does he do around 6:28 . I understand up until that point where he finds the X's what is the theroum for separating the polynomial?

    • @johnnguyen7987
      @johnnguyen7987 9 років тому

      +Max Hollander Are you talking about the zero product property? You can set all the polynomials individually to 0 and solve for the x's in the lone polynomial as long as you do it for all of them. Which is why he gets x^2 -1 = 0. And you just solve for X accordingly which is + 1 and -1. He then does the same for the 5x^2-1

  • @fatimaa1991
    @fatimaa1991 11 років тому

    You have to plot the values 1, -1, 1/sqrt5 and -1/sqrt5 on a number line like he did and then you have to test the numbers around these plotted points. So you have to find a # left and right of the plotted values and then plug them back into the 2nd derivative to see if you get a positive or a negative answer. If you get a positive answer then that means you have a concave up and a negative answer means concave down.

  • @coffeeandbjj
    @coffeeandbjj 11 років тому

    helped me out so much. thank you!

  • @tommetcalf4587
    @tommetcalf4587 11 років тому

    This is so much help, thanks!

  • @taylorrestall6717
    @taylorrestall6717 9 років тому

    Thank you so much for your videos Patrick, you've really helped me out!

  • @TonyNguyen-it7vd
    @TonyNguyen-it7vd 11 років тому

    ALL HAIL SIR PATRICKJMT!