Absolute Maximum and Minimum Values of Multivariable Functions - Calculus 3

This Calculus 3 video tutorial explains how to find absolute maximum and minimum values given a multivariable function such as f(x,y). It explains how to find the critical points using partial derivatives and how to use the endpoints of rectangle D to find the absolute extrema.
Lines & Planes - Intersection:
• How To Find The Point ...
Angle Between Two Planes:
• How To Find The Angle ...
Distance Between Point and Plane:
• How To Find The Distan...
Chain Rule - Partial Derivatives:
• Chain Rule With Partia...
Implicit Partial Differentiation:
• Implicit Differentiati...
________________________________
Directional Derivatives:
• How To Find The Direct...
Limits of Multivariable Functions:
• Limits of Multivariabl...
Double Integrals:
• Double Integrals
Local Extrema & Critical Points:
• Local Extrema, Critica...
Absolute Extrema - Max & Min:
• Absolute Maximum and M...
________________________________
Lagrange Multipliers:
• Lagrange Multipliers
Triple Integrals:
• Triple Integrals - Cal...
2nd Order - Differential Equations:
• Second Order Linear Di...
Undetermined Coefficients:
• Method of Undetermined...
Variation of Parameters:
• Variation of Parameter...
________________________________
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www.video-tutor.net/
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[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/

[@kaanaqd5636]

biggest problem of university teachers is that they don't use simple language. If they use simple words like this guy, university students won't have any problems. Thank you brother.

[@kevinpatrick8655]

so true bro

[@nikolatezzla3894]

Damn true

[@ermiasethio]

They have the knowledge but not the teaching skill ..that is the problem😢

[@sunny.w2579]

so true, man

[@evidenciachengeta6572]

@@ermiasethio very true they make things complicated

[@user-kp4wn3hy6w]

This man has saved my acamic life who knows how many times

[@drioko]

thank you for actually explaining things step by step and not having an ego like most teachers that only skip steps to prove they are better than you

[@st0rmstate]

If it’s a triangle, one side is going to be slanted so you’d need to find the equation of a line for that side (y=Mx+b) and plug that value of y in for the original equations y’s to get your new function like the other sides. Then take the derivative of that function and equate it to zero to find the critical point. Plug that critical point into that new function you found and get your value that way.

[@MustafaAli-rq9dq]

Dude, I don't know how to thank you rn. Like, even just hearing your voice has calmed me down so much while working on this problem set, your a lifesaver.

[@colehonecker6436]

you're*

[@chrisbotch3528]

@@colehonecker6436 its your

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for explaining Absolute Maximum and Minimum Values in Multivariable Calculus/Calculus Three. Although I took Calculus Three many years ago, I am still having some problems with this topic. Solving many problems is the best way to fully understand this material from start to finish. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@midnightmadness1714]

Thank God i am born in the era where this man exists and posts life saving videos. Thank God!

[@dlwlrmae]

Man you have no idea but you’ve saved my whole life. My teachers are so, so bad and I barely ever learn anything from them. You’re the only one I rely on for trustworthy knowledge 😭

[@mritunjay2624]

this dude has been helping me with my exams since 3 years now

[@jrichalot]

Thank you. I've just drowned in a 45-minute lecture at the end of which I was more confused than ever! In barely over 10 minutes you have cleared it all up. Now to watch your explanation again and make clear notes.

[@debarshiroy2939]

you are not just Organic Chemistrytutor, you are damn so good in Maths ! Ive never seen you teaching chemistry, your math vdos are simply life saving, time saving and soo simple to understand. Thank you for making these videos, Always grateful

[@odgarig8601]

This is so fun to do lol. I'm gonna spend a whole day solving these.

[@philipjarecki8643]

Its gonna be too late for me by the time you make it, but if you could for the future students out there make a video on absolute max and min of a triangle and ellipse that would be awesome

[@Thadnill]

I believe it's the same principle but you use 3 segments L1 - L3 instead of 4?

[@EnderGaming50]

@@Thadnill yeah it is

[@gigihide6974]

Same! I would love a triangle or an elipse, I am trying to do a triangle now and I am having some confusion. I cant tell if Im just missing something dumb or its just almost 1am and I should sleep-

[@elmandiliaymane7349]

@@Thadnill but in one case both x and y will be variables

[@no1channel734]

I've considered many textbooks to understand this concept, but you've explained in a simple manner. Tq sir ❤️❤️

[@ConceptualCalculus]

At about 2:50 The Organic Chemistry Tutor lists all the places where the maximum and minimum points could be. He says they could be at the corners of the rectangle (true), at some point along one of the borders (true), at the critical point he found at (2, 2) (true), "or some other point inside this region" (false). Because the region is closed (includes its own borders) and bounded (does not go to infinity in any direction) and the function f(x, y) is continuous on the region, a maximum value and a minimum value of f on the region must exist, and those values must occur either at a critical point in the interior or on one of the borders. They do not occur at some other point inside the region.

[@glowingember1466]

Thanks!

[@MM-wv4ez]

So there's no need to add that extra point (3,3) that he added to the table... correct?

[@ConceptualCalculus]

@@MM-wv4ez Not quite. The extrema can be at critical points along the borders of the region, which is what (3, 3) is.

[@elgalvin]

@@MM-wv4ez3,3 is located at L3 border

[@woodychelton5590]

But WHY though? Why can't we have them occurring somewhere else inside the region? I've been thinking about this a lot.

[@jacktrembloc9660]

This is awesome! Thank you so much! I wasn't getting it, but the way you did this helped me so much!

[@ananya4560]

man you are just the best!! thank you so much, you made me actually pass uni maths that my professors couldn't do in 4 months!!!

[@vidyanandiitbombay]

thank you sir outstanding teacher you are.love from india❤❤❤❤❤

[@asif7240]

Incredible video. Thank you so much!

[@danielnoah7284]

I learned a lot from you . Thank you so much sire!

[@user-uc7ch6lo4m]

you have saved my ass so many times you deserve the world bro

[@jinghuanxiong6525]

This video is super clear. Thank you so much!!!

[@mouseahmed778]

You are the reason of my success. I can't express words your goodness but I would like to say some words that can't be worth your goodness. You are the best best best best teacher in this world. I never forget you teacher.

[@sorayastewart4998]

This made complete sense, I tried one of my examples from class with it and got the right answer. Giving me confidence for finals

[@amournat]

literally made this problem so easy while in the textbook it looked impossible thx

[@1-__ISA__-1]

Urghhhh thank you! qwq I'm trying to learn this as fast as I can cause I don't understand the lectures and I have a quiz tomorrow. You and your videos are a blessing! Qwq

[@ventureyans4248]

Thank you so much sir..it's very quite understandable..

[@brianv62]

Awesome! Helps a lot, thanks!

[@ashmitpathania]

Best video about absolute maxima and minima🙌

[@jesuslorenzo557]

you're awesome, thanks!

[@Lactosian]

Predicting that this definitely helped me for my test tomorrow

[@tf_aerostorm5010]

Thank you so much, actual life saver

[@stevemwanza7521]

Well explained 🫡

[@magaplex6476]

Brilliant video! I do have a curiosity though, what if the region is a circle or ellipse?

[@princessvalles2281]

I love you! Thanks a lot!

[@muhammadseyab9032]

very nice video thank alot

[@user-fi6mz2tc4s]

Thank you!

[@alizehkhan1157]

Good work please keep it up

[@mmq6525]

I think I understand you better than my teacher because my teacher has to prove why we can do this, then teach it. You just go right into the process of how to do it without any proving which makes it very easy to learn. It's nice to understand the proof in class, then have a good procedural video like this to go over. In-depth understanding at its finest.

[@anderiabarzanji7354]

saved my life god bless ur soul

[@gabrielafuschini9078]

Thank you!!

[@owenanderson4913]

I am doing a very similar question however I am being instructed to enter the numbers of the edges (L1,L2...) into the dz/dx and dz/dy equations opposed to the non-partially derived f(x) equation and I wanted to know why. What changes? does it make it easier?

[@aadithya.a3935]

bruh my exam starts at 2pm and i am watching this at 10.00 am .u really helped me so much tqsm :)

[@rohitsinghbhau1060]

What if, there is any negative value of function, then should we have to consider negative or mode of it as in question absolute is mentioned

[@kamrankhankami7793]

love you sir

[@ericedvardsson5577]

what differs dose it make if it increases or decreases?

[@proxy8918]

bless your heart

[@matheusgrandinetti2657]

Absolute god of calculus.

[@user-pq6jq4gd6q]

my finfinalsalls in tommorowsaving thank you for saveing me form failing

[@crazyjester993]

Table will be already given or if not given we can select random pairs until I get maxima, minima and saddle.

[@RinaNewhouse]

30 minutes before exam LET'S GO!!!!

[@yousufhaidari6319]

thanks bro

[@zeyad7947]

quick question, once you had the critical points why didn't you just plug them all in back into the main equation. why did he do all those steps in the middle?

[@neen9099]

❤️‍🔥❤️‍🔥❤️‍🔥😍 thank you !

[@Ella-is4pl]

I don't hate math, I just don't have you as my teacher

[@shraddhasubedi3792]

what if the x or y side of 'L' doesn't equivalent??

[@Mohamed-dy7rx]

Legend

[@lorensworldgottalent4238]

2x is also means two 1x factors.

[@salmankhanumrani213]

Table made my life easier

[@rabolaimotinyane6315]

why do all this l1 thing when we can just plug in our point and see which values is actually the min and which is the max

[@rafiakhalid4999]

Please help me solving: Find the absolute minimum and absolute maximum of f(x,y)=x^2-y^2+xy-5x on the region bounded by y=5-x^2 and the x-axis.

[@raandkapilla]

Why did u find that (3, 3) point I didn't understand that part.

[@yasinsohail6206]

Yar aik chumi idher r aik udher ap ki waja se kal ka mera paper bach jaye ga💕

[@kanivakil198]

7:51 "Now because we have a quadratic..."

[@fauzansyauqi2815]

why

[@gijs6560]

?

[@mattnaka6437]

Is (2,2) a saddle point?

[@whereswaldo1376]

From my calculations, it is, since the determinant of the Hessian matrix is negative.

[@liquidoxider]

I love you

[@Nukroo]

7:20

[@falah834]

But you haven't found abs min/max in the region, you just evaluated along the boundary

[@Too_media]

is there any one who knows the organic chemistry tutor's face?

[@shanzehimran9324]

We got a quadratic equation in L3, why do we use it? it seems really random. Like none of the points were derived from the derivative of an equation we made from the line segments. Also we plugged (2,2) into the original equation, why didn't we just do it for the rest of the points?

[@biggusdickus1792]

You have to check it just to make sure it isn't the real Abs min or Abs max

[@pavese1379]

Thank God I speak english, math videos in my native language are usually very boring and uninteresting.

[@ansharora3248]

Great Content. Could you just add a sign to like your videos? I always somehow forget to do that...

[@rekipa7579]

You missed a critical point fx = 2x-2y =0 gives (0, 0)

[@017_ihsan_muhammadihsanami3]

istg i love u so much no homo

[@lorensworldgottalent4238]

That was obstructional

[@ejdaniels2463]

My friend keeps telling me that the pythagorean theorem has not yet been proven.......whos down to help me jump him

[@christianroylammawin9136]

Yes true because it is just a theorem, it is not a law, ex. Law of Gravitation..

[@ejdaniels2463]

Not you too :,(

[@user-wq7dv3vs3p]

تفضل : ) www.cut-the-knot.org/pythagoras/index.shtml

[@mathimorlythewhaleshark4245]

Suppose there was a triangle. It has sides a b c as hypotenuse. If you had four of them aligned so all the b is lined with a, and c formed square that is c^2. The square the triangle made has equation (a+b)^2 or a^2+2ab + b^2 and it equals c^2, the swuare. The triangle is 1/2bh or 1/2ab and there is 4 so 4(1/2) is 2 2ab+square in middle of c^2 is the same as the whole square a^2+2ab+b^2=c^2+2ab 2abs minus so a^2+b^2=c^2

[@tamsaasoo5418]

fucking legend

[@John-wx3zn]

your 4 and y look the same. fix it.

[@quinnopdencamp490]

ur y look like 4 bro

[@cyb3r_81]

bro all u had to do was plug it into the equation

[@gandalf7769]

No because then you would have missed the point (3,3) which could have been an abs min or max

[@cyb3r_81]

@@gandalf7769 oh yeah.

[@cyb3r_81]

@@gandalf7769 i missed that earlier

[@wakaboomnick]

Dude shoulda just studied mathematics or physics. The superior form of chemistry ;) . Just a lil joke.... No , but really dude.

[@xarran]

How about absolute min/max for x, y ∈ R?