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

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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:

Angle Between Two Planes:

Distance Between Point and Plane:

Chain Rule - Partial Derivatives:

Implicit Partial Differentiation:

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Directional Derivatives:

Limits of Multivariable Functions:

Double Integrals:

Local Extrema & Critical Points:

Absolute Extrema - Max & Min:

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Lagrange Multipliers:

Triple Integrals:

2nd Order - Differential Equations:

Undetermined Coefficients:

Variation of Parameters:

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Final Exams and Video Playlists:

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

yaxsilanroy
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the future of society is dependant on this man

chamba
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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!

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

gl
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how did he find those three points at the last problem (14:34) (0, 0) (1, 1)(-1, 1) . I know that he said plug in 0, 1,-1 but I'm not sure why he did that.And where did he get those values to plug in

johnathantran
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How do you find the points of interest though? When your partials have both x and y in them, I mean

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

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

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

tuguldurr
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P(2, 2) is local max not min, u contradicted yourself.

ethanwagner
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on the second question, how did you determine that those were the points of interest?

memorynkhoma
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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.

HB-nwcb
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the point (2, 2) should be a local maximum because fxx is negative and D is positive!

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

oliviaw
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Aight imma watch this whole channel before finals lol

ochiroo
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İn my opinion you are wrong in first example. Because there are should local max(Atəşə salam)

elnar
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On the second example, why do we chose (0, 0), (1, 1) and (-1, -1) as our points of interest?

juanduarte
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You have saved me countless times in all of science and math, although you have an error which everyone is pointing out. You are the best

tumelolebepe
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You made a mistake fxx<0 and D>0 it's not local min but local max

khwababamkhuseli
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hey friend, love your work always and forever but please check your solution to the first question. Should be local max.

jessblair