Concavity introduction | Using derivatives to analyze functions | AP Calculus AB | Khan Academy

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  • čas přidán 27. 08. 2024
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    Sal introduces the concept of concavity, what it means for a graph to be "concave up" or "concave down," and how this relates to the second derivative of a function. Created by Sal Khan.
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Komentáře • 71

  • @aristrudel8017
    @aristrudel8017 Před 10 lety +95

    I absolutely love how you repeat things twice. "As you can see the slope, the slope is negative, is negative." Makes this entire video better.

    • @adamahmadpour8036
      @adamahmadpour8036 Před 5 lety +2

      its the exact opposite for me, i get annoyed watching these videos because he always repeats things. Like bro i got it

    • @NewWesternFront
      @NewWesternFront Před rokem +2

      go get the papers get the papers

    • @RayyanKhanRayyanKhan
      @RayyanKhanRayyanKhan Před rokem +1

      @@NewWesternFront Sal Two Times

  • @picklesandcheese1997
    @picklesandcheese1997 Před 9 lety +26

    you are doing great things in this world, teaching kids many things that certified teachers can't even teach us...keep doing what your doing khan :) !!

  • @CaliBoBali22
    @CaliBoBali22 Před 8 lety +15

    Wow I have been studying derivatives for over a month and didn't really understand what they were until I watched this video. The way you lined up the graphs made so much sense. I finally had that lightbulb moment and I can now say that I understand derivatives. Thank you thank you thank you!

  • @valeriealcaraz9018
    @valeriealcaraz9018 Před 8 lety +30

    khan academy is a beautiful thing

  • @AddictedtoGeneralHos
    @AddictedtoGeneralHos Před 11 lety +4

    Greatly summarized all of the little things that I couldn't catch in my 50 minute lecture in under ten minutes... Amazing

  • @kevynlub2655
    @kevynlub2655 Před rokem +1

    concavity was a mystery for me but giving all the graphs like side by side really helped me to fully understand it. You are always goated man, never stop being a savior to all of us lost sheep

  • @lilcuku
    @lilcuku Před 11 lety +3

    You are uploading these perfectly in sync with the topics that we are coveringin my AP Calc class! :D I LOVE YOU!!

  • @ItsEvanWilson
    @ItsEvanWilson Před 4 lety +3

    WE’RE LEARNING KHANCAVITY ON KHAN ACADEMY

  • @jessicasingh001
    @jessicasingh001 Před 8 lety +13

    I wish you were my calc professor

  • @ian.ambrose
    @ian.ambrose Před 3 lety

    What a God of math. Jeez, your brain is out of this world.

  • @KuleTube
    @KuleTube Před 7 lety +83

    Concavity... more like Khan-cavity amirite?

  • @shyaamsundar2262
    @shyaamsundar2262 Před 2 lety +1

    Awesome man , idk what to tell !! Ur a god for self learning people ..Nice explanation good job

  • @TommyCarstensen
    @TommyCarstensen Před 11 lety

    I'm sure you can find the curriculum from various US universities by doing a search on the internet. I think the Khan lectures are mostly aimed at high school students in the US and across the world. He is a great teacher! I would like to build an army of Khans and send them to all corners of the world :)

  • @iMacBoy91
    @iMacBoy91 Před 11 lety +5

    This is very entertaining :)
    But I've got a question, is this taught at US universities?

  • @lilysawi4849
    @lilysawi4849 Před 6 lety +3

    god bless this man

  • @techgirl1312
    @techgirl1312 Před 8 lety +1

    Salman khan, you are a gift to us. Can you do more computer science video?

  • @minjaeeeeee
    @minjaeeeeee Před 6 lety +3

    math is beautiful

  • @sanjaym6080
    @sanjaym6080 Před 11 lety +3

    It's KHANcavity!!!! Thanks Sal for your wonderful videos.....

  • @whysomad6338
    @whysomad6338 Před 10 lety

    @صطفىالعبيدي‎
    It's taught in Canadian high schools, probably the same in the US

  • @MLOpsBasics
    @MLOpsBasics Před rokem

    Didn't knew even being positive slove can decrease....thanks..

  • @sameedansar3552
    @sameedansar3552 Před 2 lety

    JazakAllah khair 👍🏻

  • @MLOpsBasics
    @MLOpsBasics Před rokem

    Simply what i needed....

  • @520_metal
    @520_metal Před 5 lety

    very concise explanation, thank you

  • @vijaybhoi8317
    @vijaybhoi8317 Před 5 lety

    Beautiful teaching sir .nice.

  • @ahumanbeing748
    @ahumanbeing748 Před 3 lety

    OMG Thank you so much.

  • @sanjeebroytonmoy686
    @sanjeebroytonmoy686 Před 3 lety

    This video is a love.

  • @JohnnyMontilla
    @JohnnyMontilla Před rokem

    OHHH YEAHHHHHHHHHHH

  • @pessimisticinpink3506
    @pessimisticinpink3506 Před 4 lety +1

    this is giving me 2011 glow bowling vibes

  • @bolajiadedasola6369
    @bolajiadedasola6369 Před 3 lety

    I love khan academy 💕

  • @pvdkatadka508
    @pvdkatadka508 Před 3 lety

    Really useful

  • @Nooreazy
    @Nooreazy Před 10 lety

    Khan keep up the good work

  • @yourroyalhighness6297
    @yourroyalhighness6297 Před 6 lety +1

    How come does the slope decrease while the graph is going to a relative maximum point, and the slope still decreases after it went through the rel max point? 4:09

    • @zy8753
      @zy8753 Před 3 lety +1

      That part confuses me too and I feel holds me back from entirely grasping what he explained and shown so well, but the closest I can get to "getting" it is that the tangent lines if drawn on the f(x) graph lie ABOVE the graph. You probably already get it, but that's my interpretation (for now), until I really get why that is what it is.

    • @MikeWilliams-ej3du
      @MikeWilliams-ej3du Před 3 lety +1

      The curve is getting less and less steep in the upwards direction (decreasing slope) as it approaches it's relative maximum and then after reaching the rel. Max. it starts to become increasingly steep in the downwards direction (decreasing slope) hence the decreasing slope until it reaches the point of inflection where the 2nd derivative becomes positive and the curve becomes concave up

  • @brianbc4
    @brianbc4 Před 5 lety

    wow you solve my 2 days problem in 10 min

  • @PatriciaPayumo06
    @PatriciaPayumo06 Před 5 lety

    Thank you

  • @suryanshushukla701
    @suryanshushukla701 Před 5 lety

    Thanks

  • @MrGUSARIK
    @MrGUSARIK Před 11 lety +7

    isn't "concave downwords"is called "convex"?

    • @uzair3690
      @uzair3690 Před 4 lety +3

      Convex upwards

    • @iranjackheelson
      @iranjackheelson Před 3 lety +1

      So did you figure out in the past 7 years whether "concave downwards" = "convex"?

    • @ian.ambrose
      @ian.ambrose Před 3 lety

      @@iranjackheelson rude lol

  • @jonathanlim1521
    @jonathanlim1521 Před 5 lety +2

    5:38 derivative derivative derivative what

  • @rajsingh8372
    @rajsingh8372 Před 2 lety

    Does concave up is same as convex?

  • @OkThisllbeMyName
    @OkThisllbeMyName Před 9 lety

    ANYONE SEEING THIS PLS HELP THIS IS URGENT
    say i'm approximating an area under curve (area between the curve and the x-axis, bounded by, say x=1 and x=10) using trapezoidal rule
    when the curve is concave upwards (2nd derivative is +ve), the area is over-estimated right?
    but what if the curve is below the x-axis when eg 1

  • @priyasachdeva217
    @priyasachdeva217 Před 6 lety

    Great 👍

  • @ludwigtroeng1808
    @ludwigtroeng1808 Před 2 lety

    Concave upwards is the same thing as convex, right?

  • @jonatanleandoer9006
    @jonatanleandoer9006 Před 3 lety

    concave upwards is the same as convex right?

  • @MrBallistae
    @MrBallistae Před 11 lety +2

    "Concativity" :)

  • @johnc7214
    @johnc7214 Před 9 lety

    HANG ON A SECOND...
    IF y(x) = sinx
    then y'(x) = cosx
    and y''(x) = -sinx
    I agree with the first graph, but the third graph Sal puts up doesn't correspond with the first graph. the third graph should be an upside down sine graph.

    • @Bryggyth
      @Bryggyth Před 9 lety +2

      I know I'm a month late, but I believe that the graphs are actually y(x) = x^3, y'(x) = 3x^2, and therefore y"(x) = 6x
      There is obviously some form of shift, because the graphs do not exactly match up, but those are the proper shapes and therefore could be a very similar graph.

    • @DaleMitchell1367
      @DaleMitchell1367 Před 8 lety +1

      +Bryggyth Definitely not x^3

    • @kavitachugh1833
      @kavitachugh1833 Před 6 lety

      3rd graph is not properly made ......it should be graph of -sin x .......correct me if m wrong

    • @gabor6259
      @gabor6259 Před 6 lety +1

      Guys, he did it ON A SMALL INTERVAL, so it's not gonna be -sinx.

    • @thetheoreticalnerd7662
      @thetheoreticalnerd7662 Před 4 lety

      How does the first graph look like a sin(x) curve?? Take sin(0) and find out :) (it should be 0)

  • @ARC-mp6cd
    @ARC-mp6cd Před 5 lety

    SAL KHAN sounds like SHROUD

  • @MRJ3991
    @MRJ3991 Před 9 lety

    how did u get the 2nd derivative ??

    • @PoesiaCosmica
      @PoesiaCosmica Před 9 lety +2

      by differentiating the first derivative :)

  • @veigar1235
    @veigar1235 Před rokem

    ❤❤

  • @ummehafsa1181
    @ummehafsa1181 Před 3 lety

    Anyone in 2021

  • @Lauderdalesfinest954754
    @Lauderdalesfinest954754 Před 11 lety +1

    I Aint Going To [Prizm]..! Lol

  • @klokdeth1
    @klokdeth1 Před 5 lety +1

    The place where garbage college teachers send you to "learn" the next lession.

  • @MinaFreshhh
    @MinaFreshhh Před rokem

    Your so all over the over the place it was so hard to understand!

  • @RobbyBoy167
    @RobbyBoy167 Před 8 lety +2

    simillrrlly

  • @Mike_Wazowskii7
    @Mike_Wazowskii7 Před 3 lety

    ...what?

  • @justsomegirlwithoutamustac5837

    I luv u

  • @Thegamemakur
    @Thegamemakur Před 11 lety

    Khancave

  • @abhikbhattacharya1130
    @abhikbhattacharya1130 Před 7 lety +4

    Khancavity 😬😬😬