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".
Khan-cavity?
lol
bol
Why American are saying concave upward and downward ? There word for it concave and convex !
Nobel Prize! This guys teaching style should be studied and taught to other teachers. Very effective, thank you!
I SEE THE LIGHT
thank u khan academy
god bless
May Allah give him the best reward. Ameen !!
This is the best stuff about mathematics i have ever saw. Sal you are a true teacher of nations just as Comenius.
You're correct. I made an annotation to reflect this.
hello sal
Hi
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!
You are the best. You explained so important points that aren't even mentioned in my textbook!!!
concativity isn't a word...just saying...
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
I've learned more in 13 minutes then I had listening to my teacher for the past two weeks.
10 years and Khan academy is the best, thank you
Two dislikes? Really? Sal teaches better than most math instructors I've come across, and there are actually people who dislike this?
This is a very good explanation of the intuition of the 2nd derivative test. Thank you
Very useful to see all of this information integrated visually. 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
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
concave up - like a smirk
concave down - like a frown
Thank you so much. This helped clear up the concept very nicely.
Very useful video... Nice work... Your channel focus on basics... Very nice...👍👍
Really good video. I have learned a lot from you.
Thanks so much for teaching!!
Great choice of colors and presentation!!
Khan Cat Ivity
Y'all need to chill just take the lesson and thank the man=)
Like always...You are THE BEST!!!!!!!!!!!
Well explained. Thank you!
Very informative. Thanks!
Over the course of my college mathematical studies, Sal has become my best friend.
Concave up like a cup, concave down like a frown.
not like frown like cap!!
tq a lott... u are helping more than i thought...
great video as always sir
thank you so much mr khan! :')
Thank God for the Internet.
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 :( .
awesome u made it so simple im so happy
just a gr8 video.... love it
today I have a calculus test and that helps, tnx
Great video!
4:36 I like that, "becoming less negative" xD
can i give this man a hug
You explain this better than my teacher :D
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
Thank you for specifying "over a domain"
This video is beautiful
Thank you sooooooooooooooooooo much!
I love learning about kahncavity
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)
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 💀
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?
Thanks a lot!
Finely explained
THANK YOU!!!!!
Finally I get it !!!!
thank you!
Ur a beast bro
who care's about the incorrect terminology...still an excellent video. Thanks
Love u mate
You explained better than my Hindu professor.
most colorful video so far...
i love khan academy!! :D
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!
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 sir
i get it now! finally ;_;
awesome
@stevenafcstanton: just find the calculus playlist on the channel page and play it. it plays the videos on sequence :)
so are you saying that anytime the interval is concave up, x>0?
brilliant
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
Hey Hrs. Calculus period 2!
What kind of tablet/notepad does Sal use to write on the black background?
i love chan academy
What program is he using now?? It used to be MS Paint like in the last vid but now its different
I've always wondered if you actually write using your mouse or if you have a stylus/pen with a touchpad.
how would i sketch a f(x) if its second derivitive is a curve not straight line(f''(x)).
Note that the second positive derivative is a sufficient condition for concavity upwards, but not necessary.
@hannahpaslabanane HAHAH Same hereee. love them both
@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.
Concativity or Concavity?
+Nawal Bashir should be concavity
I was wondering! thank you :) *****
up like a cup (concave up) down like a frown (concave down)
thought my teacher is great till i watched ur video.....
people are complaining about concativity and concavity, and here i am, never heard of those two words before😂😂😂
the one person that dislikes this video has a concave down life haha.
me like it
In case off moduluy function how we check concavity..point of inflection
Modulus
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?
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..
Concavity
I always called it concavity.
FCKK TQQ SO MUCH
more generalised is even derivative changes sign ... then it is point of inflection... because it's not 2nd derivative always
Khancativity.
@fieryred411 One year later, another sad little boy is following your path. About to be 1:00 am on a school night now. Again.
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".
can cavity i'm CRYING
Seems like Sal had a cold!
I've never heard the word "concativity" ... is it supposed to be "concavity"?
thanks for the math, now I'll teach you english... CONCATIVITY!!!
Khan- cativity