7:01 "Concave upwards is like a 'U', concave downwards is like uh...uh,I guess uh,uh, uh... An upside down 'U'!" Haha... Thank you so much for the great videos!
great explanation, I think this would be even clearer if the graph was annotated with the the values of dy/dx ie showing the values increasing of decreasing if you dont mind me saying
Concave upwards - (Thumb up) - the U shape (glass) can be filled with beer increasing slope (fun) Concave downwards - (Thumb down) - the U shape (glass) cannot be filled with beer decreasing slope (fun)
Thanks for the video!! So helpful But i 've got a question, so is it true or false that if f "(x) = 0 at x=c, then c is a point of concavity? If false why?
yeah, khan academy makes studying more efficient AND you actually understand the content rather than just memorization at khan academy. I'm replying 9 years later XD
+Doofan Udendeh @brandon singh What Brandon said is correct..don't be confused here...when you draw a straight line joining the two points of the curve, and then when the curve is below that line, then it is convex... E.g. f(x,y)= xy is a convex curve..check it..
i know this is a late reply. just for ur own sake.. when he said x increasing around 3:50.. he meant that when its concave up the slope increases, because when you move from left to right the (x) increases. for instance -1 is higher than -4 or -5... so going from -4 to 1 "the x increases".
Nobel Prize! This guys teaching style should be studied and taught to other teachers. Very effective, thank you!
This is the best stuff about mathematics i have ever saw. Sal you are a true teacher of nations just as Comenius.
I SEE THE LIGHT
thank u khan academy
god bless
Khan-cavity?
lol
bol
Why American are saying concave upward and downward ? There word for it concave and convex !
@@zadramm1 I agree. Americans' way of studying mathematics in high school is a bit stupid.
*Khan-cativity
You are the best. You explained so important points that aren't even mentioned in my textbook!!!
May Allah give him the best reward. Ameen !!
Two dislikes? Really? Sal teaches better than most math instructors I've come across, and there are actually people who dislike this?
I can't thank you enough man. Hope someday I have enough money to support your work and pay you back for everything you've done
7:01 "Concave upwards is like a 'U', concave downwards is like uh...uh,I guess uh,uh, uh... An upside down 'U'!" Haha...
Thank you so much for the great videos!
Very useful to see all of this information integrated visually. Thank you
You're correct. I made an annotation to reflect this.
hello sal
Hi
10 years and Khan academy is the best, thank you
This is a very good explanation of the intuition of the 2nd derivative test. Thank you
I am not just math but also English from you as I listen. Then, of course, teaching skills and conversation skills 🤣
Thank you
Over the course of my college mathematical studies, Sal has become my best friend.
Great choice of colors and presentation!!
Thank you so much I've been trying to understand this for so long and this was so freaking helpful god bless you
Very useful video... Nice work... Your channel focus on basics... Very nice...👍👍
Concave up - like a cup
Concave down - like a crown
+Shine13373 Up=Smile
Down=Cry
up - happy
down - sad
Concave up like a cup. Concave down like a frown
can i give this man a hug
Really good video. I have learned a lot from you.
Thank you so much. This helped clear up the concept very nicely.
Thanks so much for teaching!!
concativity isn't a word...just saying...
concave up - like a smirk
concave down - like a frown
You explain this better than my teacher :D
Like always...You are THE BEST!!!!!!!!!!!
Y'all need to chill just take the lesson and thank the man=)
great explanation, I think this would be even clearer if the graph was annotated with the the values of dy/dx ie showing the values increasing of decreasing if you dont mind me saying
Well explained. Thank you!
Concave upwards - (Thumb up) - the U shape (glass) can be filled with beer
increasing slope (fun)
Concave downwards - (Thumb down) - the U shape (glass) cannot be filled with beer
decreasing slope (fun)
great video as always sir
today I have a calculus test and that helps, tnx
tq a lott... u are helping more than i thought...
Very informative. Thanks!
just a gr8 video.... love it
Concave up like a cup, concave down like a frown.
not like frown like cap!!
awesome u made it so simple im so happy
Thank God for the Internet.
who care's about the incorrect terminology...still an excellent video. Thanks
great thank you my teacher would not do a bitter job than this
One letter, can change the entire meaning of a sentence.
***** hell yeah!
i had a test on this earlier this morning, but for some reason i tend to understand things sooo mucj more after a test. which is already too late :( .
I love learning about kahncavity
This video is beautiful
Great video!
You explained better than my Hindu professor.
4:36 I like that, "becoming less negative" xD
Thank you for specifying "over a domain"
this is very importante notion and you can apply it every where.
very veryy how to think where we can see this notion in practical field
thank you so much mr khan! :')
Finely explained
Thanks for the video!! So helpful But i 've got a question, so is it true or false that if f "(x) = 0 at x=c, then c is a point of concavity? If false why?
You make studying the night before for the final a viable option
yeah, khan academy makes studying more efficient AND you actually understand the content rather than just memorization at khan academy. I'm replying 9 years later XD
Khan Cat Ivity
Note that the second positive derivative is a sufficient condition for concavity upwards, but not necessary.
most colorful video so far...
@stevenafcstanton: just find the calculus playlist on the channel page and play it. it plays the videos on sequence :)
I've always wondered if you actually write using your mouse or if you have a stylus/pen with a touchpad.
it's pronounced CONCAVITY!!!
+ironslay3r99 YEAH XD
right!
John Doe
Then why the fuk are you writing correct language?
That was a good critism not harassment you chump
It's even written so!
I know right 💀
Concativity or Concavity?
+Nawal Bashir should be concavity
I was wondering! thank you :) *****
Hey Hrs. Calculus period 2!
up like a cup (concave up) down like a frown (concave down)
i love khan academy!! :D
Ur a beast bro
I don’t understand why we need the second derivative to tell us the slope I positive can’t see see that from the first derivative?
Thank you sooooooooooooooooooo much!
Thank you sir
What kind of tablet/notepad does Sal use to write on the black background?
how would i sketch a f(x) if its second derivitive is a curve not straight line(f''(x)).
more generalised is even derivative changes sign ... then it is point of inflection... because it's not 2nd derivative always
awesome
so are you saying that anytime the interval is concave up, x>0?
Finally I get it !!!!
Thanks a lot!
thought my teacher is great till i watched ur video.....
What program is he using now?? It used to be MS Paint like in the last vid but now its different
people are complaining about concativity and concavity, and here i am, never heard of those two words before😂😂😂
i love chan academy
THANK YOU!!!!!
I've never heard the word "concativity" ... is it supposed to be "concavity"?
In case off moduluy function how we check concavity..point of inflection
Modulus
Why not use displacement, velocity and acceleration concept which is lots more intuitive rather than use slope
brilliant
the concave downwards is equivalent with convex right?
yep it is
+Selrond no it is not -_- convave downwards is concave.... concave upwards is convex
+Doofan Udendeh @brandon singh What Brandon said is correct..don't be confused here...when you draw a straight line joining the two points of the curve, and then when the curve is below that line, then it is convex...
E.g. f(x,y)= xy is a convex curve..check it..
thank you!
What do mean by x is increaisng?
i know this is a late reply. just for ur own sake.. when he said x increasing around 3:50.. he meant that when its concave up the slope increases, because when you move from left to right the (x) increases. for instance -1 is higher than -4 or -5... so going from -4 to 1 "the x increases".
@fieryred411 It's 4:01am and i have an 8:10 class tomorrow. I mean today. Oh snap...
And i second that I love you.
What is an inflection circle ?
Love u mate
Seems like Sal had a cold!
I was spelling it as colclativity.
😂😂😭😭
@hannahpaslabanane HAHAH Same hereee. love them both
@fieryred411 One year later, another sad little boy is following your path. About to be 1:00 am on a school night now. Again.
I always called it concavity.
can cavity i'm CRYING
Where is the next video link ?
i get it now! finally ;_;
When I'm up I smile. When I'm down I frown. Who am I?.... x
whaaaat...............???????????????????????????????????
thanks for the math, now I'll teach you english... CONCATIVITY!!!
Khan- cativity