Local extrema and saddle points of a multivariable function (KristaKingMath)

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Local extrema and saddle points of a multivariable function (KristaKingMath)

Рет қаралды 643,420

Күн бұрын

► My Partial Derivatives course: www.kristaking...
Learn how to use the second derivative test to find local extrema (local maxima and local minima) and saddle points of a multivariable function.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
FACEBOOK // / kristakingmath
TWITTER // / kristakingmath
INSTAGRAM // / kristakingmath
PINTEREST // / kristakingmath
GOOGLE+ // plus.google.co...
QUORA // www.quora.com/...

Пікірлер: 646

@undeadman7676 3 жыл бұрын

College is very quickly turning into a place that tells me what I need to learn as opposed to actually teaching it to me. These videos are life savers.

@kristakingmath 3 жыл бұрын

I'm so glad I've been able to help! :)

@443810 2 жыл бұрын

That is a point of college.

@ZaidKhan-uc9jh 5 жыл бұрын

what is this sorcery ? I understood every word

@OmerAhmedIT 8 жыл бұрын

Simply perfect, your maths, pronunciation, video quality, audio quality. Everything is perfect. Thanks a million!

@kristakingmath 8 жыл бұрын

+Omar Alshaker You're welcome, I'm glad you liked it!

@asamonson6866 7 жыл бұрын

You are the reason thousands of students pass calculus I,II,III. Thanks.

@regularkid414 5 ай бұрын

9 years of videogap and still your explanation taught me better than anyone. Thank you very much 🖤

@kristakingmath 5 ай бұрын

Awwwww you’re so welcome!! I’m honored to be able to help!! ❤️❤️❤️

@regularkid414 5 ай бұрын

@@kristakingmath Glad to find a good youtube tutor now that I'll need it for a year now 👋.

@cobraigmoments 6 жыл бұрын

I just want to say thank you teacher. I followed every videos of yours in partial derivatives. I gave my college few days back. it's all thanks to you that I performed so well.

@kristakingmath 6 жыл бұрын

I'm so happy I was able to help!

@Max-ii3pj 8 жыл бұрын

I told my professor to watch Krista.

@khalilfarahvlogs3941 6 жыл бұрын

MIMBUBA she is smart

@rubabzehra3146 4 жыл бұрын

I did that too 🤣

@jasan_roy 4 жыл бұрын

😂😂😂

@Hema_vlog7 3 жыл бұрын

😅😅😅

@learnwhileathomewithharkir3072 3 жыл бұрын

Hahahaha👍👍👍

@bboygadget 9 жыл бұрын

I cannot explain how simple it was to follow this for my calculus exam tomorrow. Thank you very much!

@kristakingmath 9 жыл бұрын

+bboygadget I'm so glad I could help!

@JannatRiyatahasin 6 жыл бұрын

You just explained such a complicated thing so simply!!! I wish all professors could explain like this. Life could be so easy!!

@albertcousin9831 6 жыл бұрын

OH MY GODNESS THANK GOD KRISTA KING IS HERE !!! i'm french and even though you speak kinda fast it's really understandable thank you

@lemonboiii9897 4 жыл бұрын

you're better than most professors on my uni. thanks a lot for this!

@amruthavalli1260 3 жыл бұрын

Actually ur writing is crystal clear which makes it more interesting to listen to!

@kristakingmath 3 жыл бұрын

Thanks, Amrutha, I'm glad you found it interesting! :)

@amruthavalli1260 3 жыл бұрын

@@kristakingmath 💜 keep going!

@CodSock 7 жыл бұрын

By far the best explanation I've found on youtube, thank you so much!

@kristakingmath 7 жыл бұрын

Aw thanks! I'm glad you liked it. :)

@pawatjoy9669 4 жыл бұрын

My whole class in 10 minutes! Thank you from Thailand 🙏🙏

@sullyflynn8746 7 жыл бұрын

Way better than my university lecturer.

@beccaprunty3971 8 жыл бұрын

OMG i seriously think you just saved my life for this midterm i have today! i could not understand this concept anywhere else i looked but watching this video made it so simple! thank you!!!

@kristakingmath 8 жыл бұрын

+Becca Prunty You're welcome, glad I could help! Good luck on your midterm, I hope it goes great!

@intrepid35sweden 8 жыл бұрын

My god, I really needed this! I've been searching for information of what the determinant of the jacobian would indicate what kind of point it is for like a week and this really helped! I've kinda just been going after the gut feeling for what kind of point it is (visualising it) and gotten it right most of the time but now I can be certain! THANK YOU!

@kristakingmath 8 жыл бұрын

That's awesome! Being certain is a much better feeling, lol :) ... so glad I could help!

@SwaggahDontStop 9 жыл бұрын

You're my favorite Calc KZfaqr. The way you explain it, and write it down is magnificent.

@kristakingmath 9 жыл бұрын

Aw thanks!

@jonrogers7844 3 жыл бұрын

You are a brilliant teacher, I was struggling with stationary points for multivariate derivatives, couldn't find a simple explanation for days, you taught me in 10 mins! You're awesome!

@kristakingmath 2 жыл бұрын

Thank you so much, Jon! I'm so glad the video cleared this up! :)

@EinPiannist 9 жыл бұрын

I subscribed to your website last week. I just HAVE to say that you are a way better teacher than Khan Academy. You get the point across to me in every single video, and your online quizzes/notes..etc have greatly benefited me. Because of you I am passing my Calc class in college. Thank you!

@kristakingmath 9 жыл бұрын

That's awesome, I'm so glad you're doing well in your class! Thank you so much for letting me know; it makes me so happy to know that the Academy has been helpful!!

@roxymang1 9 жыл бұрын

This question is straight out of my textbook! I was stuck on the last part and this video helped so much :D

@raphaelpimenta 5 жыл бұрын

Wooooow years trying to find someone so straight to the point!! Amazing thanks million!!!!!!

@RadhaRanjanMadhav 4 жыл бұрын

I last studied Calculus in college around 15 years ago, but this made me understand the concept fully. Thanks for a very clear explanation.

@kristakingmath 4 жыл бұрын

You're welcome, Radha, I'm glad it cleared things up! :)

@martynsnwaokocha6982 4 жыл бұрын

I've subscribed to your channel this was 11 minutes of well spent time. Thank you for the straight to the point lesson

@kristakingmath 4 жыл бұрын

Thanks for the sub, Martyns!! :D

@ashm192 2 жыл бұрын

Oh my god thank you!!! I have been trying to make sense of this for a while now and I have a test in it tomorrow. I'm currently dealign with an online Calc 3 class and its terrible, there is no professor to explain concepts. This was a life saver!!

@kristakingmath 2 жыл бұрын

You're welcome, Ash! I'm so glad it helped, and I hope the test went great! :)

@jeremydolphin7823 3 жыл бұрын

The way you explained this made it so much easier thank you so much

@kristakingmath 3 жыл бұрын

You're welcome, Jeremy, I'm so glad it made sense! :D

@errbodylovesme 9 жыл бұрын

You're the real MVP! Thanks

@zaibysheikh4317 5 жыл бұрын

Gurl you go! You made it all so easier for me! I literally have 2 days till my Cal 2 final exam and i swear i needed to understand alll topics so bad! Now i feel like im saved! Yay! God bless you always! ❤

@kristakingmath 5 жыл бұрын

I'm so glad it helped, Zaiby! Good luck on the final, I hope you do great!! :D

@zaibysheikh4317 5 жыл бұрын

Haha expecting the same but krista i have one question. Is iterated integral and double integal same thing? If not then whats the difference. Please clear my doubt im confused

@zaibysheikh4317 5 жыл бұрын

And one more thing. Is implicit partial diferentiation and implicit differentiation also the same thing?

@dmitrikorin3033 7 жыл бұрын

I was worried you were one of those tutorial videos that have a huge distracting section on the screen reserved for you face or other stuff and i'm glad this is a khan academy (in some ways even better) quality tutorial. Thank you, it's really hard to find people like you.

@kristakingmath 7 жыл бұрын

Thanks for the feedback! Glad you liked it!

@professorbrohi 2 жыл бұрын

It's 7 years old video but still useful for college students.. Wonderful explanation 🥰🥰🥰

@kristakingmath 2 жыл бұрын

Thank you so much, I'm so glad you liked it! :)

@guitarttimman 4 жыл бұрын

You simplify everything so nicely Krista.

@norlinans Жыл бұрын

You know what, you not only clever but your voice really attractive too!!! I love your accent, your pronunciations and u really inspired me to become a lecturer. Thank you so much for making tutorial videos and I love all of them ❤️❤️❤️

@Mariamx 5 жыл бұрын

You explained much better in 10 mins than my professor in 2 hours. Thank you

@kristakingmath 5 жыл бұрын

Thanks, Miss! I'm so glad the video was helpful! :D

@Maffarazzo 8 жыл бұрын

This was incredibly helpful, you explained it better, faster and easier than my math professors at university!

@kristakingmath 8 жыл бұрын

+Maffarazzo I'm so glad it helped!

@zaidz6263 5 жыл бұрын

From now on you're my new teacher

@kristakingmath 5 жыл бұрын

Aww thanks, Zaid! :D

@azarel7 3 жыл бұрын

Excellent tutorial. Learnt more about the topic here than I did in class.

@kristakingmath 3 жыл бұрын

Thanks, azarel, I'm so glad it helped! :D

@Anna-qp1fi 2 жыл бұрын

The best thing about this video, is that it uses a realistic example! A lot of videos either go too easy or too hard...

@kristakingmath 2 жыл бұрын

Glad you thought so! :)

@badwolf0099 4 жыл бұрын

Look out, this channel is gonna make me learn math

@bugrahantaspnar2360 8 жыл бұрын

You are a very good teacher. You attract students' attention. Also nice examples. Thanks to you midterms are easy...

@kristakingmath 8 жыл бұрын

+Bugrahan Taşpınar Thank you very much!

@TinyMaths 4 жыл бұрын

I've already covered this and am now practicing it. I really like the way you set everything out, because it made it much easier to navigate to the values you need when you needed them. For instance I like how you wrote out the first and second and mixed derivatives with their corresponding values at (a,b) before using the matrix method for finding 'D', so you just had to plop the values into the matrix. And then when you needed to check the specific nature of a stationary point you just went back to the values attributed to those points derived from the first order derivative. It might be second nature to you, but my process can get into such a mess and I sometimes get confused about where to look for the required values. Your process was so easy to navigate and that's what I got from your video most of all.

@kristakingmath 4 жыл бұрын

I'm so glad it helped! Sometimes in math the hardest part is just staying organized and not losing your place in the problem. So any time you can set up your formulas ahead of time, like you said, I think it can be a big help to make sure you stay on track! :D

@1105comfortablynumb 8 жыл бұрын

Great explanation. Very clear. Thanks. Now on to Lagrange multipliers:)

@kristakingmath 8 жыл бұрын

Nice! :)

@Falkjar 8 жыл бұрын

Thanks! I got an A on my final. :)

@kristakingmath 8 жыл бұрын

+Falkjar That's awesome! Congratulations! :D

@mdjaved100 9 жыл бұрын

I loved your explanation! You made it so easy. I don't know why authors they don't understand the way of writing in the book so that students can understand !

@kristakingmath 9 жыл бұрын

I'm so glad this made sense and was helpful!

@kidfrase 7 жыл бұрын

Well, now I won't fail my test. Greatly appreciate this video and all the others you have made. Thank you!

@kristakingmath 7 жыл бұрын

I hope you rock the test! I'm glad the videos are helping. :)

@maturdizballing8019 Жыл бұрын

I have test tomorrow and this is really helpful. Thank you so much

@gokay9490 9 жыл бұрын

That's awesome. I have an exam about 2 hours later and i got this thanks to you. Yup!!!

@kristakingmath 9 жыл бұрын

gökay umutlu Hope the exam goes well!

@isaiahmumaw 5 жыл бұрын

I'm really bad at focusing during lectures, videos like these are incredibly helpful!

@kristakingmath 5 жыл бұрын

Oh good! I'm so glad the videos are helping! :)

@thenofma 7 жыл бұрын

Thank you saved me. PS you're better than my university lecturer

@jebril 6 жыл бұрын

Most of the online tutors are...makes you wonder. I've seen random tutors on Chegg better than 90% of actual professors.

@user-vg6qh1nb1s 9 жыл бұрын

Wow… . you are very well at explanation this subject… . I hope you upload more practice examples on that 😊

@glamzen266 9 жыл бұрын

Wow amazing explanation! Thanks a million. I wish my teacher would explain like you!

@Crystalleyes321 3 жыл бұрын

Krista you are a KING

@MomentsWithLuh 7 жыл бұрын

Thanks a lot Krista. Lots of love from South Africa!

@kristakingmath 7 жыл бұрын

You're welcome! Glad you liked it. :)

@lostchee-lj7ie 4 жыл бұрын

So much better than my lazy ass online professor who just covers simple examples out of the textbook thank you! Fr fr

@dont_trust_any1_even_ur_waifu 9 жыл бұрын

ty, my teacher's straight outta russia so i dont show up to class -university of maryland

@dont_trust_any1_even_ur_waifu 7 жыл бұрын

it means i cant understand her because she has a thick accent. for example, she may or may not be a good teacher but i simply do not know because of this. also update, i ended up getting an A in the class (went to lecture once and never came back - just showed up for tests / quizzes)

@claystar9valor 6 жыл бұрын

I'm trying so hard to get an A in my applied calculus class. I've always sucked at math so it'll be a miracle if I pull it off.

@FreakyEagle13 6 жыл бұрын

Hard to understand the dialect gap. The same way that an American sounds funny when attempting to speak russian.

@FreakyEagle13 6 жыл бұрын

Yo I'm in college park right now taking calc 3. Cheers bro

@Honest-King 6 жыл бұрын

I still can't get a C+ in any calc ... Maybe diffrentials & linear algebra will be easier ..

@michaelpartyka7289 9 жыл бұрын

Great video, very helpful. Thank's a lot. 1000x clearer than my textbook.

@kristakingmath 9 жыл бұрын

+Michael Partyka Glad you liked it!

@16colombiano 8 жыл бұрын

0 to 100 real quick

@tendo99v 5 жыл бұрын

@aamirbangash985 5 жыл бұрын

100

@spag5296 5 жыл бұрын

real

@alexanderkollmann9612 5 жыл бұрын

quick

@paids3764 5 жыл бұрын

lol ^^^^

@Shaziya12 10 жыл бұрын

hey:) i have a test in two days, and i study from your videos, they re really helpfull. Thanks a lot:)

@kristakingmath 10 жыл бұрын

i'm so glad they help! good luck on your test!! :D

@Pv2Bagbar 7 жыл бұрын

Thanks so much, you broke this down into extremely easy to follow steps.

@kristakingmath 7 жыл бұрын

Yay! Glad it could help. :)

@alur_chip8271 Жыл бұрын

i missed the class on this and i have a quiz tomorrow i owe you my life

@rpatil0009 4 жыл бұрын

Thank u very much mam, I did not understood this concept in class but after watching this video I am confident enough to solve such problems.

@kristakingmath 4 жыл бұрын

Oh good! I'm so glad it helped and that you're feeling confident with these problems now! :D

@yoshidownload 6 жыл бұрын

Bless your soul Krista that was so helpful

@kristakingmath 6 жыл бұрын

Oh good! I'm so glad it helped! :D

@fleetfantasy 9 жыл бұрын

Fantastic video, couldn't understand before, now understand completely! Thanks very much :)

@mds00 6 жыл бұрын

amazing... learned more in 10 min from her than 6 hours in my calc 3 course.

@nicolerojas9207 2 жыл бұрын

You are saving me ! It doesn't have to be so complicated. Thank you!

@kristakingmath 2 жыл бұрын

You're welcome, Nicole, I'm so glad it helped! :)

@oskarremvang1226 3 жыл бұрын

Amazing video! Straight to the point, super easy to understand. Saved me before my test :D

@kristakingmath 2 жыл бұрын

I'm so glad to hear that, Oskar! I hope the test went great! :D

@lkmdojiurge9urgieurh 5 жыл бұрын

Solid video! Simplifies a very difficult concept. My only suggestion would be to show the hessian matrix and use the Fsubxx Fsuxy notation as its easier to work with

@guitarttimman 4 жыл бұрын

Negative acceleration means slowing down to a point. The MAXIMUM point which will not be at the origin and that means a negative slope. Think of a parabolic function in the first quadrant. Speeding up means the slope is rotating to the right and approaching zero. A minimum. Speeding up and slowing down is determined by the change in acceleration which is the second derivative of a position function. Do you see where I'm going with this Krista?

@ankithsaranjit 4 жыл бұрын

This is best explanation I have ever had.

@lukajevtovic8250 4 жыл бұрын

Thanks for this lesson, it was of great help! One thing I'm still struggling with, though, is how to evaluate a critical point if the quadratic form is equal to zero. I know you're supposed to evaluate the infinitesimal increments of the function at those points, but it's usually very briefly covered, if at all, so any help on that subject would be great!

@milesjohnson5482 5 жыл бұрын

Thank you for this incredible tutorial!

@jasonvegan5761 4 жыл бұрын

Wonderful lesson, would give anything to be back in live classrooms again but I'll gladly take this instead, thank you for the explanation!

@NazZimou 6 жыл бұрын

Your voice makes math more pleasant to study lol, you should replace Morgan Freeman and narrate movies

@agentmikster44 6 жыл бұрын

Oh boy, this is even better than Khan Academy Easily subscribed, liked, and all that stuff

@kristakingmath 6 жыл бұрын

Thank you so much, I appreciate it! :)

@ossu2428 5 жыл бұрын

WORLD CAN NOT DESCRIBE HOW MUCH THANKFUL I AM SO I USE CAPS : THANK YOU !!

@kristakingmath 5 жыл бұрын

You're welcome, Ossu! :D

@HashemAljifri515 Жыл бұрын

Your explanation is phenomenal!

@anjalidinesh7767 7 жыл бұрын

Crystal clear explanation , I understood it perfectly, Thank you.

@kristakingmath 7 жыл бұрын

Thanks! I'm glad it could help.

@sharonsolana 3 жыл бұрын

Thank you for explaining it so well Krista! That was a math workout!

@kristakingmath 3 жыл бұрын

You're welcome, Sharon! I'm so glad it all made sense! :D

@imrankhan-uo4jy 4 жыл бұрын

After watching your videos multivariate calculus is just a piece of cake.

@Vision_Voyagers 6 жыл бұрын

We get two values of X that is 0 and 2 and two values of y that is 0 and 1 for some reason you have taken the point (0,0) and (2,1). But if we take point (0,1) (2,0) we get D=-144 on both points.

@akshatkharema1569 3 жыл бұрын

She is just an angel😭😭..... thankyou so much

@kristakingmath 2 жыл бұрын

You're welcome, Akshat! I'm happy to help! :)

@onkenkqwili9471 8 жыл бұрын

you are amazing Krista

@Nick-om3tz 9 жыл бұрын

Very good explanation. This info will be helpful on my Calc 3 exam this week. Thank you very much :)

@kristakingmath 9 жыл бұрын

Thanks! Good luck on your exam!!

@dannyasti7493 5 жыл бұрын

I finally get it! Thank you Krista you saved my exam!

@kristakingmath 5 жыл бұрын

I'm so glad it helped, and I hope the exam went great!! :D

@azeemabdulrasheed2701 2 жыл бұрын

this video is a lifesaver lol,having sem exams tmrw

@crod1232 4 жыл бұрын

Great video! I have one question... at 10:08 you say that we need to see if the second derivative with respect to x is negative or positive in order to see if we have a max or min at that point. Is this always true? Why dont we use the second derivative with respect to y?

@cabdirisaqboos961 5 жыл бұрын

What an outstanding explanation.. Amazing Krista

@apaturia 8 жыл бұрын

You are just about to save my ass from my upcoming calculus exam... I will for sure look through all your videos! /Natalie from Denmark

@kristakingmath 8 жыл бұрын

+Natalie Nanette Willadsen Rock that exam Natalie!

@anjalisoni5837 5 жыл бұрын

watched like 100 vids before this one and this finally got to the point.

@naudikhan8314 5 жыл бұрын

yes..finally. ..

@mds00 6 жыл бұрын

@Krista King, I got an A in my calc 2 because of you. I was doing very poorly till I started watching your videos. I think college professors try to act too smart and over complicate things.

@muhammadosama8308 5 жыл бұрын

Might be late but really good and easy video to learn this topic.Big thanks

@kristakingmath 5 жыл бұрын

Thanks, Silver, so glad it helped! :)

@iMoczus 9 жыл бұрын

You're better than my teacher Ivan! God Bless You!

@kristakingmath 9 жыл бұрын

+Matthew Moczarny I'm glad I can help!

@robertbielitz9834 9 жыл бұрын

+CalculusExpert.com seriously, I love your voice. It puts me at ease. :)

@Peter_1986 8 жыл бұрын

+CalculusExpert.com Wouldn't it be more general to use the Hessian matrix in order to identify the critical points? That method can be used for functions of more than two variables.

@afreenyousaf2104 7 жыл бұрын

awesome explained by you...nice voice...now I am ur FAn...thanks a lot....From Pakistan

@cornerbloke8861 3 ай бұрын

Hey Krista, GREAT video, thanks a lot!! But I've got a question thay I am a bit afraid to ask tbh bec. I suspect that the answer of it might be very complicated xD. Why did we used partial derivative of x and not y to figure out whether the extremum point is a min. point or a max. point?

@unnavaanurag 8 жыл бұрын

you are just a life saver .....i got O grade n my finals...thanks

@kristakingmath 8 жыл бұрын

+unnava anurag You're welcome, I'm so glad I could help!

@yackawaytube 10 жыл бұрын

Great video. I suggest doing an example with where f depends on more than 2 variables and explain the use of eigenvalues (aka positive definite vs negative definite matrix) in that case.

@Discostu1997 7 жыл бұрын

Great video! you made it so much easier on me! Now off to write my exam!

@kristakingmath 7 жыл бұрын

I hope it went well!

@countdracula2192 8 жыл бұрын

Thanks a lot for this video. I'm English, but my study is in French. I don't have the luxury of understanding everything. At least not, until I watched this video.

@kristakingmath 8 жыл бұрын

+Dark Bean I'm so glad it helped!

@diffindo8421 4 жыл бұрын

omaigosh. I understood everything. I cannot thank you enough.

@user-gu4tw2uf6s 5 жыл бұрын

I’m confused (10:29) as to why we had to find 432 when we couldve just looked at 12 from the beginning. What made us look at 12 in the first place?

@mattkrcma4092 5 жыл бұрын

First we have to make sure the value of D is greater than 0. If D is less than 0, then it is a saddle point which is neither a max nor a min. Again, D=f_xx*f_yy - (f_xy)^2