Curve Sketching Using Calculus - Part 2of 2

[SynpaticInc]

Thank you so much Patrick! You've been a great help throughout the semester and now as I'm reviewing for my family. Your videos are beautiful; your explanations are clear and easy to understand. If you ever write a textbook or manual let us know as I'd love to use that to supplement my classes!!

[free1here]

isn't the graph still right? that's concave down from infinity to 0

[parmi4i]

Awesome videos! But I just had a question, when you are finding the inflection points and you use a number that's less than one, lets say -1, shouldn't that be 2((-1)-3)=-8/(-1)^4)=-8? So you get a concave down? If not please explain because I don't get it otherwise!

[999m4em]

you are the best! thank you!!!!

[physicistinthemaking]

How do I know y=0 as a horizontal asymptote only applies on (-infinity,0)U(1,infinity)? ie. the curve crosses y=0 at (1,0) but can't cross it anywhere else... I guess I don't understand how it is an asymptote when the curve crosses it.

[jmartr34]

Hey can you recommend any studying techniques? Great videos!

[patrickJMT]

@jmartr34 read, do problems, re-read, do more problems

[iiottoii]

If your HA is 0 then why does your graph cross 0?

[patrickJMT]

@iiottoii a graph can cross its horizontal asymptote

[Khizzzzzy]

i love you pat.

[masterchief9064]

thanks heaps man, my maths class is wayyy behind the other class and i had to catch up over the weekend. your vids helped heaps!

[BadAceBarker]

The broken cap on his marker is driving my OCD self crazy!

[Cancer98765]

You said your final graph would be wrong, but isn't it actually correct? Your mistake in arithmetic was of course wrong, but your graph is still right from what I can tell.

[na9oooooooor]

=3

2:17

Got it ?!

:p

[na9oooooooor]

=3 

:p

[dhaval712]

when you did the concavity, on the left side of 0, isn't its suppose to be concave down instead of concave up because when u plug in -1 into the equation, the answer will be -8. At least thats what I think it should be.

[Crossoverzz]

do porn

[Raymondlk]

Your the best !!

[kforsyth31]

2((-1)-3) does not equal a positive number...

[bking0704]

Final Cal Exam 2mrw, now i'm READY xD !

[MultiMoe91]

is the new video uploaded or not yet?

link me please

thanks in advance

and patrick i love you

[EdBogie]

If I get a 5 on my AP exam, it'll all be because of you.

[dghansen85]

Just so you know the correction dont show up on my iPhone. So for the 3 of us that watch these in public have that to worry about.

[billyo1989]

YOU.ARE.AMAZING.



[2030587]

You are extremely helpful!! thank you so much... you explain in a very simple way and not many can do that

[missdillpickle]

THANK YOU THANK YOU THANK YOU!!!

[Jkun]

Am I the only one who was gonna see some awesome movie of some guy doing calculus and ending up with a ''sketch'' of a woman's curves? >.>;;

~Jkun~

[skyfaze]

i have bent sharpies too : 0

[Clipster15]

I got a test in the next few hours on this. Though sucks because none of the functions I have to sketch are going to be as simple as this one. Same idea, yes, but more prone to stupid mistakes, YES! Good video.

[maxiswitty]

hi, why is there no local min?

[kevinwiz]

i don't understand why 0 isn't an inflection point?

[vamosrogerfederer]

@kevinwiz theres a VA at x=0 there can't be anything there.



[eMCRutz]

by the way it wasnt a mistake, it's still concave up, since the denominator would also give a negative, so in the end you still get a positive, concave up.

[ZombieGadget]

@eMCRutz Incorrect, because x^4 would make the denominator positive. Now if x was raised to an odd number, then it would give a negative value.

[Sylvanas17]

ur awesome!!!!!!!!!

[fuarddy]

hey patrick im from malaysia...great vids, i got a test tomorrow hope i can ace it from studying your vids......

[patrickJMT]

@fuarddy good luck!!

[alexspoy]

@fuarddy I am from Malaysia too.. in Multimedia university, Melaka.. I used to study from Patrick's video a lot!

[smartaleck05]

I caught that mistake you pointed out, too :)

Great job. You're videos really help to clarify what I partially understand.

[GeneralLee721]

The graph is actually correct. I used my graphing program to double check. Only the table that said that from negative infinity to 0 is concave up is wrong but you can see that he draw a concave down in that interval so it's all good.

PS. NEVER STOP DOING VIDEOS.

[TheDude541]

Dear Patrick, I think I love you now.

[poohkah3]

this helped me soo much! thank youU!!!!!!

[Morelloo1]

im scared of cos and sine ones.

[mws123]

i really wish this guy was aloud to post vids > 10 minutes.

[patrickJMT]

@mws123 i can now do that. but i think shorter is better often times. people will not watch long videos (most people that is)

[webmastertool]

@patrickJMT Yeah i know, there are these like hour long MIT videos with even more info but i see most people have no interest in watching them.

[therab00]

thanks so much.

can u do some more examples please

[iraqiya1991]

For every exam so far i've used ur videos. I was considering dropping the course and changing majors till i found these. ur a life saver. Thank You so much!!!!

[1789Mikaela]

Thank You So Much!!!! U R MY LIFESAVER!!!!!

btw: U teach way better than my prof.

[yukyisan]

I dont understand when you did your second derivative and you used 3 in which aren't you suppose to use the critical #'s as ur intervals? I'm so confused.

[etismyname]

@yukyisan

the 3 is to get the zero for the numerator

[shahzebahmed1990]

at the end how come the second line does not stop for the horizontal asymtote??

[vicb0t]

who else has a calc test 2mrw?

[patrickJMT]

@vicb0t not me!

[Jsebas289]

@vicb0t I DO!

[iraqiya1991]

@vicb0t

Me. :( Hate calculus. thank god for youtube!!only way im passing it. lol

[vicb0t]

@iraqiya1991 i dropped calc a few days ago cuz i didnt find his vids in time... :/

[hondai]

@vicb0t Mine is today :P

[JSasRays]

@vicb0t i have one in 30 min. skipped school to watch some youtube vids on calc

[vicb0t]

@JSasRays im retaking this shish!

[Jenuvio]

@vicb0t LOL!! XD

[2030587]

@vicb0t hell yeah, tomorrow- on a friday -_- i guess no fun fun fun fun for me lol

[blaze4404]

Your graph still turned out correct even though you made that concavity error. when determining the concavity you did make an error saying it was concave up, but then during the process of sketching you corrected yourself saying it was concave down.

[MissKorky]

Thanks for your help!!(:

what website can we find more or ur videos?!

[patrickJMT]

@MissKorky you can not post urls in comments, but my website is on my channel page

[snipermule6]

WHY ARE YU A LEFTY!?!??!!

[jay2yosi]

you r superp , Great teacher ! I am learning a lot from your video. Thanks a lot!

[arual1969]

OMG IT IS SIMPLE!!!!!!!! 

[MsRach77]

thnks alotttt!!!!!!

[xerxes0129]

Are you a maths professor?

[SiksGameRuns]

i know the interval from negative infinity to 0 of the second derivative is wrong, but isn't the graph right anyway? or am I missing a point?

[Hillumamu]

Man, the interval from - infinite to 0 of the 2nd derivative is wrong. You wrote it's positive man.

[Santana2163]

@Hillumamu Yeah I see it too...

[paperairplanes18]

i don't know why i bother going to class. this is all i needed... much better than a "read your text book" session with my teacher

[mynameishmay]

thank you so much

[starwarsfreakdood]

why does the graph cross the horizontal asymptote

[guylaroche5]

@starwarsfreakdood

cross over point probably

[ClownDatWalk]

The graph has a possibility to cross the HA, even tho its a HA

[jazzysax102391]

@starwarsfreakdood A function can cross a horizontal asymptote as long as it approaches said horizontal value as it goes to infinity, it cannot, however, ever cross a vertical asymptote.

[tesla737]

if im rich all my money will be given to you ;)

u have single handedly saved me from failing

[lpbl2004]

Thanks Pat, Ive been watching all of your videos, and they've helped alot...

[taginiho]

thanks a million patrick, these videos really helped

[xkrnaaax]

wait. at 2:46 when you plug in the -1 into the double prime function isnt that supposed to be CD since its a negative over a positive?

[xkrnaaax]

nvm apparently everyone else caught it lol. my bad. great videos anyway!

[blacknikeboy]

is there a video for sketching and interpreting derivatives and the second derivative?

[julub]

dont stop doing videos

[p0wnztv]

I thought the concavity from negative infinity to 0 was concave up? But the graph is concave down from negative infinity to 0. Not that it will ever reach 0 but I thought it would look different based on the information.

[ver0mg]

hello, thank you for the video. I have a question, I am trying to obtain infexion points what should I do when in f I plug in the value that I obtained solving f '' and it results undefined? f(x)=f ' (X )= (-2x^2)+x+3) / (x+2) and f '' (x)= (-14(x+2)) / (x+2)^4 Does that mean that there are not inflexion points?

[13Nog]

The graph seems correct to me either. You made a mistake back there but didn't draw it wrong at the end. I'd do the same sketch.

btw, thanks for doing that. Helped a lot.

[manjula85]

Question, u said there is a HA at 0, if that is the case there couldn't be any pts on the x-axis right? so how is it that we get an intercept at x=1? (I understand how we get that intercept, but it technically doesn't make sense).

[Kay0Bot]

I know you made a mistake with the concave section but isn't that still the correct sketch?

Can you please do a video for curvilinear?

[Kloosterman01]

yeah its almost correct.. at the right corner it should be down down like on the x axis sort of thing..

but still thank you for this, your doing a great thing for this world dude!! =P and trust me my mom always says.. be nice to the nerds.. becasue one day youll be working for one.. =D

[manjula85]

I think so too, he said concave down from (-infinity,0)

[CaptainCarthex]

That still is the correct sketch.

[Khmer22cambo]

thx alot man, u made it so easy to understand!! Short, simple and clear! Thx

[magic100172]

sorry i accidentally rated 4 stars..intended to click 5 ..

[term2121]

dam thank god for ur videos.. my teacher is british and tries to be funny when he teaches... he says the same joke over and over again in class and the retard nerds laugh at it everytime...

[patrickJMT]

i would probably laugh too

[whynos666]

im gonna take for second time calculus math 2 at college again :(

but with ur vids, and practicing a lot im gettin better :)so im going to past with high scores the next time :)

[techlance]

Thank you so much Patrick...I now love curve sketching thanks to your video.

[nbanour]

I loved this video and it saved my time of trying to understand this lecture by myself

Thanks a lot for this nice ,helpful ,and clear video

again thanks a lot

[lildragonblue]

I love you *3* very useful videos. I have a terrible prof this semester, he doesn't even know what he's doing, so this is a huuuuuuge help to clear things up :)

[illa2015]

wait i don't understand why the graph isn't correct still, what is incorrect?

[mi07ke]

i think the graph has been corrected, this is what the graph should look like (the first part is concave down, decreasing) before he said it was concave up. Im pretty sure he made the correction already.

[robinvwhelan]

this is so nice of you to do for people. it really helps a lot. when im feeling too lazy to study myself and write out notes i can jut watch these!

[Kloosterman01]

dude just dont die! you saved my bacon, i didnt udnerstnad this stuff at all until i wtached this video,! thank you!

[jayz098]

what does it mean when your criticals numbers from your first derivative are the same as the second derivative?i have a local minimum i found from the 1st der. but the same critical number showed up in the 2nd der.

[danny4213]

than you so much.... this was very helpful...

[initialg]

I hate curve sketching. The process is so tedious.

[joeKing7]

could u do another sketch example...without the mistake :) please?

[patrickJMT]

yes, plug it into the original. after all, we are trying to find inflection points on f(x); the first and second derivative just help to tell us where to 'look' on f(x)!

hope this helps!!

[quynhho2002]

So when you find the inflection number, you plug that into the ORIGINAL equation to find the y-coordinate of an inflection point, not the first derivative, right?

Thanks Patrick! [:

[Freedomboy006]

amazing explanation.. u saved me from failing my test tommorow

[patrickJMT]

good luck on your test!

[JackEffenBauer]

P-diddy, you're my savior for my calc test tomorrow thanks a lot!

[patrickJMT]

good luck on the test!

[vash01000100]

this is making my calc class so much better

[cookyhat155]

when you plugged in -1 for the concavity of the second derivative, shouldn't it be 2(-1-3)/1=2(-4)/1=concave down?

[patrickJMT]

yes, you are absolutely correct, thanks!

i will add annotations now thanking you!

thanks!

[leebh]

Wonderful. Keep up the great work Patrick!!

[patrickJMT]

i will do my best : )

[Draco488]

Great video Patrick! A nice clear explanation, what many students of Maths are after I believe :)

[patrickJMT]

howdy! i am trying to give you what i think is helpful, or what was helpful to me at least! glad that you all like it : )

[MATHGEEK1989]

Great Explanation! Thanks for the help!