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Local Extrema, Critical Points, & Saddle Points of Multivariable Functions - Calculus 3

The Organic Chemistry Tutor

992,725 views

This calculus 3 video explains how to find local extreme values such as local maxima and local minima as well as how to identify any critical points and saddle points in a multivariable function such as f(x,y).

Lines & Planes - Intersection:
How To Find The Point Where a Line Interse...

Angle Between Two Planes:
How To Find The Angle Between Two Planes

Distance Between Point and Plane:
How To Find The Distance Between a Point a...

Chain Rule - Partial Derivatives:
Chain Rule With Partial Derivatives - Mult...

Implicit Partial Differentiation:
Implicit Differentiation With Partial Deri...

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Directional Derivatives:
How To Find The Directional Derivative and...

Limits of Multivariable Functions:
Limits of Multivariable Functions - Calcul...

Double Integrals:
Double Integrals

Local Extrema & Critical Points:
Local Extrema, Critical Points, & Saddle P...

Absolute Extrema - Max & Min:
Absolute Maximum and Minimum Values of Mul...

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Lagrange Multipliers:
Lagrange Multipliers

Triple Integrals:
Triple Integrals - Calculus 3

2nd Order - Differential Equations:
Second Order Linear Differential Equations

Undetermined Coefficients:
Method of Undetermined Coefficients - Nonh...

Variation of Parameters:
Variation of Parameters - Nonhomogeneous S...

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

Full-Length Videos and Worksheets:
Patreon: collections

20 Comments

@TheOrganicChemistryTutor Creator 2 years ago Pinned

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

@chamba149 5 years ago

the future of society is dependant on this man

@SacheinRoy 6 years ago

Fxx=-6 ; Therefore it is local maximum as Fxx<0 is local maximum. This is the correction. Do check out 6:04. Thanks.

@ArchieUplifts 1 year ago

CORRECTION AT 6:04. IT IS A LOCAL MAX

@zeyad7947 5 years ago

this guy has been carrying me since sophomore year in High school (chemistry) then junior year (algebra & chemistry) then senior year (calc 1 and physics) then 1st year of engineering in a few classes and now in second year of engineering. YOU ARE A LIVING LEGEND!

@gl291000 6 years ago

For problem one it should be local max. D < 0 and fxx(a,b) < 0 , then f(a,b) is a local maximum.

@tuguldurr 6 years ago

How is this youtube channel better than my school wtf am i doin with my life?

@oliviaw6397 3 years ago

5 hours before my calc final. i owe this man my life 🙏

@kaneshp5688 7 months ago

28 mins before my calc final. i owe this man my life

@AOTglobal28 1 year ago

The first example, the point should be a local max since according to the rules or conditions you gave at the beginning of the video, which is (if D > 0 and fₓₓ < 0)

@owenwu9600 6 years ago

this guy has saved my life countless times. Im not even religious but god bless you

@mallows-s1o 1 month ago

This channel helped so many students graduate (it helped me pass my calc class otw to finish calc 3), goated channel

@ab-cm2ic 1 year ago

For those who didn’t get 8:24
8(x^3-y)=0
>x^3=y......(1)
Now
8(y^3-x)=0
>x^9-x=0 (plugged in y=x^3 from 1)
>x(x^8-1)=0
>x=0, x^8-1=0
x=+1,-1

@TheLifeOfMarcus 4 years ago

IDK who you are but I hope your beautiful YouTube videos are letting you live life on a yacht somewhere in the Caribbean. You are amazing bro. I'm going to university where I get hella confused, and come home to watch your videos which are AMAZING and help me understand the content more. Nothing but love bro!!!

@HB-nw2cb 6 years ago (edited)

Your channel is so helpful, I don't even go to the lectures anymore. I just watch your 15-30 min videos and it saves me 2 hours of commuting to and from uni only to attend a lecture I don't gain anything from.

@AskMeSTEMQuestions 6 years ago

Shouldn't (2,2) be a local maximum? Since fxx is negative?

@labrinth9432 4 years ago

i dont usually write comments.....but i had to thank you....keep doing this

@imanichristian523 4 years ago

im not gonna lie, math been having me fight for my life in the arena for the last couple weeks. thank u so much for this video. gonna secure atleast B because of your help. u a real one.