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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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.
its the exact opposite for me, i get annoyed watching these videos because he always repeats things. Like bro i got it
go get the papers get the papers
@@NewWesternFront Sal Two Times
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 :) !!
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!
khan academy is a beautiful thing
Greatly summarized all of the little things that I couldn't catch in my 50 minute lecture in under ten minutes... Amazing
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
You are uploading these perfectly in sync with the topics that we are coveringin my AP Calc class! :D I LOVE YOU!!
WE’RE LEARNING KHANCAVITY ON KHAN ACADEMY
I wish you were my calc professor
What a God of math. Jeez, your brain is out of this world.
Concavity... more like Khan-cavity amirite?
Awesome man , idk what to tell !! Ur a god for self learning people ..Nice explanation good job
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 :)
This is very entertaining :)
But I've got a question, is this taught at US universities?
god bless this man
Salman khan, you are a gift to us. Can you do more computer science video?
math is beautiful
It's KHANcavity!!!! Thanks Sal for your wonderful videos.....
@صطفىالعبيدي
It's taught in Canadian high schools, probably the same in the US
Didn't knew even being positive slove can decrease....thanks..
JazakAllah khair 👍🏻
Simply what i needed....
very concise explanation, thank you
Beautiful teaching sir .nice.
OMG Thank you so much.
This video is a love.
OHHH YEAHHHHHHHHHHH
this is giving me 2011 glow bowling vibes
I love khan academy 💕
Really useful
Khan keep up the good work
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
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.
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
wow you solve my 2 days problem in 10 min
Thank you
Thanks
isn't "concave downwords"is called "convex"?
Convex upwards
So did you figure out in the past 7 years whether "concave downwards" = "convex"?
@@iranjackheelson rude lol
5:38 derivative derivative derivative what
Does concave up is same as convex?
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
Great 👍
Concave upwards is the same thing as convex, right?
concave upwards is the same as convex right?
"Concativity" :)
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.
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.
+Bryggyth Definitely not x^3
3rd graph is not properly made ......it should be graph of -sin x .......correct me if m wrong
Guys, he did it ON A SMALL INTERVAL, so it's not gonna be -sinx.
How does the first graph look like a sin(x) curve?? Take sin(0) and find out :) (it should be 0)
SAL KHAN sounds like SHROUD
how did u get the 2nd derivative ??
by differentiating the first derivative :)
❤❤
Anyone in 2021
I Aint Going To [Prizm]..! Lol
The place where garbage college teachers send you to "learn" the next lession.
Your so all over the over the place it was so hard to understand!
simillrrlly
...what?
I luv u
Khancave
Khancavity 😬😬😬