Inflection Points and Concavity Intuition

[DanicaMarieMusic]

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!

[Iced0826]

I think ever since I heard Sal say "Concativity," I've acquired the habit of saying the exact same thing... :p

[Sappyspartan]

Thank you for specifying "over a domain"

[slimjijo123]

me like it

[hannahpaslabanane]

You and patrickJMT are saving my ass <3

[samiarox]

@hannahpaslabanane HAHAH Same hereee. love them both

[TheSelamber]

tq a lott... u are helping more than i thought...

[PSPJOHNPSP]

i love chan academy

[lautnerluvr502]

i love khan academy!! :D

[jackdestisbest]

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)

[AnotherBrownKid]

what vid is after this one?

[bluechao2]

i had a revelation when i got to 10;40 or so...

thank you for putting time to teach us kiddies!

[MrBwunch]

Don't you just calls em Parabolas? 

[tmorris09]

@MrBwunch he's just showing parabolas because they are the best examples to show if its concave up or down. most of the graphs you're going to do will change its concavity and you will have to figure out where it does

[ian559fresno]

who care's about the incorrect terminology...still an excellent video. Thanks

[ultimazer0]

Two dislikes? Really? Sal teaches better than most math instructors I've come across, and there are actually people who dislike this?

[imthechiz]

@ultimazer0 im pretty sure those were from the instructors...

[itechkid]

Over the course of my college mathematical studies, Sal has become my best friend.

[AndyJohnD1001]

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

[koketka69]

Like always...You are THE BEST!!!!!!!!!!!

[Worldclass09]

thanks from Bangkok

[fateater77777]

You make studying the night before for the final a viable option

[kenyakickz25]

the one person that dislikes this video has a concave down life haha.

[thieflord08]

wow you guys are dumb... its not a contest of who can stay up the latest watching the vids... its about learning and i can bet you that the kid that went to sleep at 130 learned more than the kid who went to sleep at like 5 because they were half asleep...

[whostheboss1983]

look at the mons pubis, that is also concave down when you are looking down at yourself

[Musiclo0ovee]

Sal you are the best in the world ...I wish you can do my exam :D

[Swimdarkenigma0]

What kind of tablet/notepad does Sal use to write on the black background?

[TheLiberalSoup]

You know, I've been thinking about something which has come about from me watching these videos. I learned the fundamentals of calculus OVER THE WEEKEND thanks to you. I didn't even know WHAT a derivative or integral was. Im in 9th grade. So, 3(?) days into watching these, it's actually caused me to be late to some of my classes. My excuse? "I was studying calculus."you are a fucking hero, Sal.

[SuperFireEagle]

You explain this better than my teacher :D

[whostheboss1983]

you can always remember if it's concave down by this rule of thumb: if you look down at yourself, your penis tip is concave down

[SleepyEyes94]

thanks god that i understand this ,

thank you :)

[Arelymelendez10]

yea i kept having to think about what he was saying... i was like have i been wrong all along??!!! but then i got it. you are very helpful by the way!! thank you

[Haseeb2]

The kids of today are very fortuanate... you have all these resources. I wish I had something like this back in high school.

[stevenafcstanton]

These videos are excellent so how do i find easily the video that follows on from this one?

[mee3012]

@stevenafcstanton: just find the calculus playlist on the channel page and play it. it plays the videos on sequence :)

[lethaltimes]

salaam bro...and thanks bro!

[susan19891231]

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?

[nuuts88]

it is great. but could u pls make the video faster and talk about the main things. i have a lot things to do and it takes me 14 mins only fot this. PLss :D

[usyflad]

What program is he using now?? It used to be MS Paint like in the last vid but now its different

[Flankymanga]

This is the best stuff about mathematics i have ever saw. Sal you are a true teacher of nations just as Comenius.

[blkstarr826]

so are you saying that anytime the interval is concave up, x>0?

[iamReynolds]

@blkstarr826 no hes saying that any time the you have a function concaving upwards, your second derivative is positive and thus f''(x) >0. That just means that the rate of change of the slope of the tangent lines is increasing at a constant (in our case) positive value.

[SamDreyfuss]

GREAT explanation ... I hope you teach.

[fieryred411]

I just stayed up till 1:30am (on a school night!) watching these videos, lol. I love you :)

[razor21x]

@fieryred411 i stayed up till 3 : 40am on school night D: (right now while i am commenting.) xD

[razor21x]

@fieryred411 its 3:40am right now while i am commenting, (On school night) too, studying for maths xD... maybe i will stay up more than this, for tommorow's exam.

[ins3rti0n]

@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.

[dashy654]

@fieryred411 One year later, another sad little boy is following your path. About to be 1:00 am on a school night now. Again.

[ychimocu]

Thanks a lot!

[fistylo]

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

[danieltian]

i always called it inflexion.

[timtu22]

I think inflexion might be a British spelling. I'm Australian, so it's what we'd use. I don't know who gave you the thumbs down for that, though, but they must be very bitter.

[danieltian]

i know eh? sore losers.

[timtu22]

You read anything British published before mid 1800s or so. Or read the glorious Sir Isaac Newton's "Opticks: or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light". From here on in, I will call anything -exions 'pioneer language' because it kicks ass.

[gtssage]

I always called it concavity.

[khanacademy]

You're correct. I made an annotation to reflect this.

[1a1a2a3a]

cool.