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:

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:

[kaanaqd]

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.

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[strmstate]

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-rqdq]

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[georgesadler]

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 YouTube TV with the Organic Chemistry Tutor.

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[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

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[philipjarecki]

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

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[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.

[odgarig]

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

[ananya]

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[jacktrembloc]

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[sorayastewart]

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