Lagrange multipliers. Chris Tisdell UNSW Sydney.

[zaleiri]

THANK YOU!

[Kyras]

This is about the tenth @DrChrisTisdell video I've watched in the past few days in preparation for my exams. Just wanted to say thanks, much clearer than my lecture notes and the Stewart book.

[brydust]

no hard and fast techniques....  just use newton's method during the exam, that will surprise your prof for sure!

[fakerneverno]

Actually what's the difference between Orthogonal Gradient Theorem and the fact that gradient is always perpendicular to a surface?

[DrChrisTisdell]

@fakerneverno One of the assumptions of the OGT is that $f$ has a local max/min, whereas to show that the gradient is perp to a surface there is not necessarily such an assumption on $f$. Great question!

[fakerneverno]

@DrChrisTisdell so basically they are the same result? but the OGT only emphasizes gradient is perp to the surface at the max/min point? then i think the OGT is redundant.

[DrChrisTisdell]

@fakerneverno The OGT is definitely needed for the proof of the method of Lagrange multipliers. It's used to show that $f$ (the function that you want to max/min) has a gradient that is perp to the surface g=0 (the constraint function) at max/min points. Of course, we also know that grad g is also perp to the surface g=0.