Local extrema and saddle points of a multivariable function (KristaKingMath)
HTML-код
- Опубликовано: 25 авг 2024
- ► 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/...
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.
I'm so glad I've been able to help! :)
That is a point of college.
what is this sorcery ?
I understood every word
Simply perfect, your maths, pronunciation, video quality, audio quality. Everything is perfect. Thanks a million!
+Omar Alshaker You're welcome, I'm glad you liked it!
I told my professor to watch Krista.
MIMBUBA she is smart
I did that too 🤣
😂😂😂
😅😅😅
Hahahaha👍👍👍
You are the reason thousands of students pass calculus I,II,III. Thanks.
9 years of videogap and still your explanation taught me better than anyone. Thank you very much 🖤
Awwwww you’re so welcome!! I’m honored to be able to help!! ❤️❤️❤️
@@kristakingmath Glad to find a good youtube tutor now that I'll need it for a year now 👋.
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.
I'm so happy I was able to help!
You just explained such a complicated thing so simply!!! I wish all professors could explain like this. Life could be so easy!!
Way better than my university lecturer.
You're the real MVP! Thanks
I cannot explain how simple it was to follow this for my calculus exam tomorrow. Thank you very much!
+bboygadget I'm so glad I could help!
you're better than most professors on my uni. thanks a lot for this!
Actually ur writing is crystal clear which makes it more interesting to listen to!
Thanks, Amrutha, I'm glad you found it interesting! :)
@@kristakingmath 💜 keep going!
By far the best explanation I've found on youtube, thank you so much!
Aw thanks! I'm glad you liked it. :)
Thanks! I got an A on my final. :)
+Falkjar That's awesome! Congratulations! :D
This question is straight out of my textbook! I was stuck on the last part and this video helped so much :D
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
My whole class in 10 minutes!
Thank you from Thailand 🙏🙏
The way you explained this made it so much easier thank you so much
You're welcome, Jeremy, I'm so glad it made sense! :D
Great explanation. Very clear. Thanks. Now on to Lagrange multipliers:)
Nice! :)
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!
That's awesome! Being certain is a much better feeling, lol :) ... so glad I could help!
You're my favorite Calc RUclipsr. The way you explain it, and write it down is magnificent.
Aw thanks!
It's 7 years old video but still useful for college students..
Wonderful explanation 🥰🥰🥰
Thank you so much, I'm so glad you liked it! :)
I've subscribed to your channel this was 11 minutes of well spent time. Thank you for the straight to the point lesson
Thanks for the sub, Martyns!! :D
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!
Thank you so much, Jon! I'm so glad the video cleared this up! :)
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!!!
+Becca Prunty You're welcome, glad I could help! Good luck on your midterm, I hope it goes great!
Wooooow years trying to find someone so straight to the point!! Amazing thanks million!!!!!!
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.
Thanks for the feedback! Glad you liked it!
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! ❤
I'm so glad it helped, Zaiby! Good luck on the final, I hope you do great!! :D
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
And one more thing. Is implicit partial diferentiation and implicit differentiation also the same thing?
Excellent tutorial. Learnt more about the topic here than I did in class.
Thanks, azarel, I'm so glad it helped! :D
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!
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!!
I last studied Calculus in college around 15 years ago, but this made me understand the concept fully. Thanks for a very clear explanation.
You're welcome, Radha, I'm glad it cleared things up! :)
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!!
You're welcome, Ash! I'm so glad it helped, and I hope the test went great! :)
The best thing about this video, is that it uses a realistic example! A lot of videos either go too easy or too hard...
Glad you thought so! :)
I have test tomorrow and this is really helpful. Thank you so much
Krista you are a KING
ty, my teacher's straight outta russia so i dont show up to class
-university of maryland
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)
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.
Hard to understand the dialect gap. The same way that an American sounds funny when attempting to speak russian.
Yo I'm in college park right now taking calc 3. Cheers bro
I still can't get a C+ in any calc ...
Maybe diffrentials & linear algebra will be easier ..
You simplify everything so nicely Krista.
Thank you for this incredible tutorial!
Wow amazing explanation! Thanks a million. I wish my teacher would explain like you!
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 !
I'm so glad this made sense and was helpful!
0 to 100 real quick
0
100
real
quick
lol ^^^^
Look out, this channel is gonna make me learn math
You explained much better in 10 mins than my professor in 2 hours. Thank you
Thanks, Miss! I'm so glad the video was helpful! :D
i missed the class on this and i have a quiz tomorrow i owe you my life
This was incredibly helpful, you explained it better, faster and easier than my math professors at university!
+Maffarazzo I'm so glad it helped!
Thank you saved me. PS you're better than my university lecturer
Most of the online tutors are...makes you wonder. I've seen random tutors on Chegg better than 90% of actual professors.
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 ❤️❤️❤️
Thanks a lot Krista. Lots of love from South Africa!
You're welcome! Glad you liked it. :)
Wow… . you are very well at explanation this subject… . I hope you upload more practice examples on that 😊
Well, now I won't fail my test. Greatly appreciate this video and all the others you have made. Thank you!
I hope you rock the test! I'm glad the videos are helping. :)
So much better than my lazy ass online professor who just covers simple examples out of the textbook thank you! Fr fr
After watching your videos multivariate calculus is just a piece of cake.
From now on you're my new teacher
Aww thanks, Zaid! :D
You are a very good teacher. You attract students' attention. Also nice examples. Thanks to you midterms are easy...
+Bugrahan Taşpınar Thank you very much!
you are amazing Krista
Bless your soul Krista that was so helpful
Oh good! I'm so glad it helped! :D
this video is a lifesaver lol,having sem exams tmrw
Great video, very helpful. Thank's a lot. 1000x clearer than my textbook.
+Michael Partyka Glad you liked it!
That's awesome. I have an exam about 2 hours later and i got this thanks to you. Yup!!!
gökay umutlu Hope the exam goes well!
She is just an angel😭😭..... thankyou so much
You're welcome, Akshat! I'm happy to help! :)
You are saving me ! It doesn't have to be so complicated. Thank you!
You're welcome, Nicole, I'm so glad it helped! :)
Might be late but really good and easy video to learn this topic.Big thanks
Thanks, Silver, so glad it helped! :)
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?
Thanks so much, you broke this down into extremely easy to follow steps.
Yay! Glad it could help. :)
I'm really bad at focusing during lectures, videos like these are incredibly helpful!
Oh good! I'm so glad the videos are helping! :)
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!
Very good explanation. This info will be helpful on my Calc 3 exam this week. Thank you very much :)
Thanks! Good luck on your exam!!
This is best explanation I have ever had.
you are just a life saver .....i got O grade n my finals...thanks
+unnava anurag You're welcome, I'm so glad I could help!
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
+Natalie Nanette Willadsen Rock that exam Natalie!
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.
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.
+Dark Bean I'm so glad it helped!
Oh boy, this is even better than Khan Academy
Easily subscribed, liked, and all that stuff
Thank you so much, I appreciate it! :)
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.
Oh good! I'm so glad it helped and that you're feeling confident with these problems now! :D
Great work! way easier to understand then my prof was!
Thanks, Sean! I'm so glad it made sense! :D
Fantastic video, couldn't understand before, now understand completely! Thanks very much :)
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.
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
You are a goddess. This helped me so much with calc 3
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?
omaigosh. I understood everything. I cannot thank you enough.
amazing... learned more in 10 min from her than 6 hours in my calc 3 course.
Thanks. I need a quick reference and refresh my memory. Your X looks like lamda sometime when you write.
your videos are saving me. THANK YOUUUU
You're welcome, I'm so glad they're helping! :D
Wonderful lesson, would give anything to be back in live classrooms again but I'll gladly take this instead, thank you for the explanation!
Thank you so much! Always better than my profs
best calc instructional videos on the web.
thank you so much!
Big thanks you just saved my exam, thanks
So glad it helped, hope the exam went great!! :D
Your voice makes math more pleasant to study lol, you should replace Morgan Freeman and narrate movies
thanks I didn't find any vedio of multivariate functions except Ur vedio
awesome explained by you...nice voice...now I am ur FAn...thanks a lot....From Pakistan
watched like 100 vids before this one and this finally got to the point.
yes..finally. ..
hey:) i have a test in two days, and i study from your videos, they re really helpfull. Thanks a lot:)
i'm so glad they help! good luck on your test!! :D
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?
Amazing video! Straight to the point, super easy to understand. Saved me before my test :D
I'm so glad to hear that, Oskar! I hope the test went great! :D
Your explanation is phenomenal!
WORLD CAN NOT DESCRIBE HOW MUCH THANKFUL I AM SO I USE CAPS : THANK YOU !!
You're welcome, Ossu! :D
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?
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
Thank you very much for your awesome explanation.
You're welcome! I'm glad you liked it!
Crystal clear explanation , I understood it perfectly, Thank you.
Thanks! I'm glad it could help.