Calculus: Graphing using derivatives

[TyTurd286]

Actually if f '' (x) = 0 you don't know what it is and have to use a sign chart. I could be a min, max, or inflection. example y= x^4.

[Advantage12]

I appreciate the videos but you seem to almost always show the conventional cookie cutter problem... But I think a lot of the time people like me come on here to find a video explaining how to solve a problem that is unlike the basic, cookie cutter problem because nobody else will show them. My question is... how would you solve something like y=x^4-6x^2 because at a point... you will not be able to factor and that confuses me as to where to go from after that point?

[zthepimp]

Sal, you are so popular! Your phone always rings during your videos.

[mirukufy]

At least "concativity" sounds like a real word. :P

Also, this is so fun. hahah.

[sam30317]

You keep pronouncing "concavity" wrong !!!!!!

[MsAllahhuakhbar]

wow the phone is ringing!....probably the telemarketer?

[paoloburbon]

thankyou so much...

[111000may]

awesome!!! :)

[6BURG9]

concativity lol...

[IMBLUESTREAK23]

So critical points are where the first derivative equals zero, and non critical inflection points are where the second derivative equals zero. Have I got that right? I'm taking the PCAT saturday, wish me luck.

[UberCuba]

i thought that when f ' ' (x) = 0 anything could happen and that its not neccessarily an inflection point. I don't know though, it just something i saw on one of JMTs videos

[ouzhanyener]

thanks alot at least i could sort it out why my lecturer didnt expalin some points

[maths486]

I have to correct something that he said.

If the second derivative of a function at a number is equal to 0, it doesn't necessarily mean we have an inflection pt. there.

take the simplest example of f(x) = x^4

f ' ' (x) = 12 x^2 so obviously f ' ' (0) = 0

but 0 is not an inflection point. In fact, x^4 is

concave upward everywhere ( the graph is always above the tangent lines at each pt. )

[MizidaKychin]

this guys is funny and educational

[Arkantosi]

Yepp, you are pretty damn king. Im good at math and always have been, but watching your vids gives me better perspective and concept. What I mean is, I now understand why things are the way they are. Is there anyway to message you for different mathquestions?

[ctw005]

I love you.

[juaneco1980]

yea I bet it was a telemarketer it's always wise not to answer the phone lol jk .

[lwilliams243]

Every student taking Calculus should know about these videos. They are great!

Thanks so much.

[ranma54]

oh boy the phone is ringing

lols

[jessicahd24]

thanks so much sal! you're the best!

[bouk98765]

love your teaching style!

[academicinfife]

I am a fellow teacher. Which program do you use to "write" on a blackboard with your pointer?

Many thanks in advance.

[academicinfife]

Thank you, netmaster96. You really got the spirit of collaboration embodied in the khanacademy project. Feel free to post more helpful and supportive comments.

[Telepcanin]

HAhahaha lol

[1a1a2a3a]

I believe he says what program he used in another one of his calc videos, im not too sure which one though....

[KCuahtemoc]

paint o.o....invert colors...and a tablet ftw.

[Painfoot]

I kind of actually explained to my calculus teacher how concave up is that the slope is increasing; he'd never looked at it like that. Calculus is really fun when it's intuitive!

[FIERYdaemon]

i did my c2 exam last week :/ shame, could have used this.

[iluvjiyongx3]

kinda diff for me, but thanks!! ^^

[Aluta37]

Thank you! This really helped me!

[batmancave009]

Thanks...a great little refresher!

[neoasd401]

thxs

[FreddyKrueger2k7]

makes me laugh "oh crap... cant do that in my head" lol. this is fairly basic, but i did pick up on that sort of "hidden" point of inflection at the non critical point.

[AkashP4]

Thanks Sal!