10 years later, the video is still helping students

Dear Patrickjmt Never and I repeat never apologize for being thorough in your explanations. It is what helps us most. Thank you for being so ridiculously accurate and amazing in teaching. :)

Guys if everyone who viewed this video up until now donated a dollar, he would have $361,374. I can't think of anyone on youtube who deserves my dollar more since he's helped me pass my classes. You rock Pat!

Patrick, you have a rare talent of explaining complicated stuff in very simple terms. Thanks!

It's funny how I got through cal 1 and 2 with patrickJMT, and now my cal 3 professor is linking us to his videos for pre-lecture.

Thank you so much Patrick. You have been the most helpful person throughout all my math courses. Calculus I - Linear Algebra/Differential Equations. You are the man!!!

iam a maths teacher in india ,my students are surprising from where our sir is bringing such a good concepts which are not given in any book, thats entire credit goes to sir patrick,keep going sir otherwise we stop at delivering. thank you very much sir.

you deserve the salary of my prof who just wasted my time explaining it in the most confusing manner that she even got herself confused

12 years later, your videos are still helping to students. Thanks a lot! @patrickJMT

your videos are very helpful & i can take my time doing my work rather than having my professor with really bad accent giving me a hard time...thanks & we ALL appreciate the help

i had so much trouble in class because our instructor didnt explain how to get the critical points very well, thank you very much, this really helped me out :)

Your catchphrase should be "Now that you've got it down Pat..." BAM a youtube legend is born.

Thank you Patrick. You are the best. I would not have survived without you. Calculus 3 - Math 20C - Linear Geometry.

Dude, i got my cal 3 test in 3 hours. Legit video, probably gonna do amazing because you explained min and max of two variables like a boss!

patrickjmt is easily the best channel for math help

thanks dude i came to the computer to play cod coz i was tried doing maths, which my weakest subject but i just searched this topic on youtube n u just made maths interesting for me.......

Thanks a lot @patrickJMT, I know I can always count on your vids to simply everything I learn in my textbook. God Bless you.

hey patrick. thanks for all your help. I've been watching your videos in my calc 1. now I'm taking calc 3. your basically my calculus professor. thanks a lot.

This EXACT problem was given on my Multivar Exam today and I had it memorized to a tee, but I chose to solve it without "copying and pasting" my thoughts on the exam. It was worth 20% of the exam too, hahaha! Thank you so much Patrick!

Guess who has a test this Tuesday and will be watching your videos for help!? *Pointing my thumbs at myself* This guy!

This video is amazing! I have my calculus final exam tomorrow and this really helped me understanding this whole concept! Thank You :)

14 years later still helping ❤😊

@patrickJMT no once they put an ad on the video your about to watch, you have to watch the ad in order to watch the video! (video factorial) video-1, video-2, video-3,...

1:40 thanks for rewriting the rules and requirements on your videos. They help ou a lot too

Test in 8 hours. Your videos are the best review for all this calculus.

With you; I don't even need my calculus book. Your explanation is crystal clear. Even I understand it :D

You explain it 100x better than my teacher!!

you turned a whole chapter in my textbook into a 10 minute video... for that I thank you greatly!!!

There needs to be a PatrickJMTAcademy, I like watching your videos better! So clear and to the point!

I'm so thankful! I've used your videos for many courses and it has always helped! Thank you very much, God bless you! :)

@prtnst glad you like them. we all have an accent to someone though. people make fun of my southern accent from time to time. that is life.

holy crap!! you are the best teacher in the whole world!!! xD sorry, i probably already posted this several times on your videos. but is the truth.. thank you very very very much.

Thank you so much for your time and energy! I wish on my next set of birthday candles that everyone would teach like you

Significantly better than my Ivy League Professors and TAs. Thanks, you're the man!

11 years later, a student has an exam tomorrow and still finds this video more helpful

relative and local are used interchangeably

Thank you Patrick! I'm watching this 1 hour before my exam hahah I got it very well thank you again!

They are already critical points. What you're checking is whether they are local maximums, local minimums, or saddle points.

I would recommend your videos to anybody doing calculus, I actually have a few times

its very good you write the rules first it helps to understand it , don't be sorry.

man you don't how much your videos helped us .. thank you !

you taught me more than my prof did! Patrick.

special thanks for writing all that down... thanks for all ur work... simply outstanding!!!

@Mathieu Nobert: redo your arithmetic; it is 1/3. You probably did this: (-2)(1/3)*(-2)(1/3)-[1-(2*2*(1/3))^2] What you should have done is: (-2)(1/3)*(-2)(1/3)-[1-(2*(1/3)-2*(1/3))]^2 You misfactored and dropped a coefficient along with its sign.

Hi Patrick you have the best concept of Mathematics.

@patrickJMT i hear ya...ppl always make fun of me cuz i stumble wen i talk...but anyways...my old professor gave the class a hard time cuz he never cared to have active teacher-student involvement. My other professors would always ask how everyone was doing as they get ready for lecture & would respond to emails...but this guy was way too stern & i felt like he didnt care that we all needed extra help...now i get help from youtube n other resources

LIFE SAVER patrickJMT

find all the local max/mins like he showed you, then plug those into the original equation and whichever is the biggest or smallest is the global max/min

Your videos are very useful to watch and learn from! I see them all the time q: )

i needed tgis so bad for tomorrow's test.. tq :)

Really thank You Sir i mean i Learn So much and it's so simple ... Peace From ALGERIA

Best Video I've seen on this so far. Helped alot.

I lvoe how the whole time your going through this probably your groaning with me like ughhh this problem is long and in my head i'm thinking the same exact thing . Haha. Thanks a lot . Your videos are very helpful and I'm a tutor for HS students and I always recomend them to you in areas they are struggling.

Is the proof for the Second Derivative test really that bad? My professor said "The proof is beyond the scope of the class." Oh, and you rock Patrick this video helps out a lot!

Thanks a lot man. I'm so glad I'm subsided to you and that you make these videos. You make calculus so much easier

I'm sorry your right you did do it right and you apparently took the time to put this on you tube. Thank you.

thank u sir..... it really helped me when could not get it 4rm the class....

@ashleytheyeti yes, you might look in the calc 1 playlist on my channel

So far I've taken the first 2 calcs only becouse of you :P Tomorrow is my third one, wish me luck :D

@hellodarlingyu u r very welcome!

at 3:18, he means to say "'Cause again, Y is a constant."

Thanks so much for these videos...You make Calculus seem so easy

@redtrex94 i do not do a ton of proofs since i figure they are in the books, but lots of people ask about them, so i may start doing that!

After so many years, THIS MAN IS STILL ON FIRE!!!

THANK YOU!! you are better than my professor.....

Exam TOMORROW !!! Thnx this helps

Funny thing is every problem my Calc 3 teacher does on the board are the exact same problems you do here. I havn't found a single problem he has done in class that you don't do in your videos.

CALC 3 test in two hours :S

dude I love ur vids!!!! u the man!! thanksss!

When you are taking the derivative of xy-x^2y-xy^2..isn't there a product rule because x is multiplied by y and x^2 is multiplied by y and x is multiplied by y^2?

Hey PatrickJMT, love your videos. Just one thing, it might have been mentioned already, but at the beginning when your giving the definition, isnt it suppose to be "When D = 0, there is no local or max min" not "When D < 0" ?? Thanks! Keep up the great videos!!

You save lives! Thank youuu! :')

wow! you make it look so simple! well explained and t's understandable! thanx buddy!

Can we test with second derivative of y in the end. Why must it be f_xx. Every youtube video including you is telling to check second derivative of x only, but never said anything about whether we could second derivative of y as a conclusion

Patric, I was lost when you use y=0 and y=1-2x and plugged into the partial Fy. You end up with x=0 and x=1 but where did you plug this numbers to get this values (0,0) and (1,0)?

These are partial derivatives, Fx and Fy

11 years later, still helping noobies

come on guys donate some money for this guy, hes the man..

God Bless you, Patrick

I really appreciate your work pat!

@martmelee you can post that as often as you wish : )

thank you very much for this tutorial. You work is very much appreciated

are the four points to check already critical points? or are u checking them to see if they are critical points?

This guy is a legend

Sir at 3 :10 you say that x is your variable and y is your constant and at 3:19 you say y is your variable. if it is a variable , shouldnt it be 2y ? Please clearify sir ! and i love your videos , please never stop making !

Given function f(x,y) = x^4 + y^4 - 2(x - y)^2, where f(x,y)≤ 0. For all values of (x,y) near (0,0), f(x,y)≥f(0,0) → At (0,0) f(x,y) has a local minimum f(x,y)≤f(0,0) → At (0,0) f(x,y) has a local maximum OK, so how do I know if f(x,y) is greater or lesser than f(0,0)??

seems like you have a video for everything i need thank you so much

What do you do when there are multiple constraints that are inequalities?

Thank you maaan you are really good in this and you should get a donation !

this is super clear, thank you so much!!!

Hey Patrick, thank a lost for posting this video. You have such a good way of teaching. I came here because after doing some homework problems, I get really frustrated when (for ex.) partial x = 3x^2-x =0. What I kept trying to do(since x has 2 values) was complete the square, but I kept getting wrong answers. Can you please explain why completing the square and factoring out x give different answers? Am I doing something wrong?

Hello, Would I be right in saying that, if you have a function F(x), with derivative F'(x), and we know that the roots of F'(x) are x=a and x=b. Then if F(a)>F(b) then we have a Max@ (a, F(a)) and a Min@ (b, F(b)), because the former is higher than than the later. Can this method of reasoning be used as an alternative to checking whether the second derivative, F''(x) 0 ? Your videos are an inspiration. Thank you.

12 years later.. still helps

@patrickJMT How about when you're asked to find "The extreme values of the given function on the indicated interval". Is that their way of asking for local/relative value? There are so many names for this stuff, it gets confusing after a while.

Actually when D=0 it could be either max/min or saddle point, but if D< 0 there are no max or min values it is alway a saddle point

am so very grateful, you have very helpful videos ..thanx N' God bless

what i don't understand is.... when finding the crit points, how do you know when to plug "x" or "y" where?

I get the impression you enjoyed teaching this problem about as much as I enjoy doing them ... and by that I mean, not much at all.

You are a god among men, good sir.

Please solve the following problem: Given y=✓x - 10x , 0 < x< 5 , prove that there is a maximum at y = 1/ 40. Please solve this problem