AM-GM inequality (1 Viewer)

[FlyingGullible]

Hi, I was just wondering since the AM-GM inequality is so useful in inequalities:
1. Is the AM-GM inequality something we'd be able to quote in an exam, or does it need to be derived everytime?
2. If not, what's the simplest/best derivation for the case of 3 terms? (I've seen a lot of different ones, what would be the most practical/easiest to remember?)

 

[Drsoccerball]

Hi, I was just wondering since the AM-GM inequality is so useful in inequalities:
1. Is the AM-GM inequality something we'd be able to quote in an exam, or does it need to be derived everytime?
2. If not, what's the simplest/best derivation for the case of 3 terms? (I've seen a lot of different ones, what would be the most practical/easiest to remember?)

1) My teacher said its not assumed knowledge and quoting it will be like using Le hopsin's rule or wotever its called...

 

[leehuan]

Do you mean that the arithmetic mean is greater than or equal to the geometric mean? (Equality iff the terms involved are the same)



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1) My teacher said its not assumed knowledge and quoting it will be like using Le hopsin's rule or wotever its called...

L'Hopital's

I wish the board would just allow it though.

 

[InteGrand]

Don't think you can quote the AM-GM inequality, so I'd recommend learning a proof for the two-variable case (very easy to prove, and very commonly needed), as well as the general n-variable case (use proof by Pólya using calculus as it is probably the quickest and is accessible for 4U students, found here: https://en.wikipedia.org/wiki/Inequ..._by_P.C3.B3lya_using_the_exponential_function (also found in the Arnold and Arnold (Cambridge) 4U textbook)). You can then write out these proofs before (or after) using the inequalities.

 

[Physicklad]

really? im pretty sure you can quote that. you cant quote it if it is indeed what you are trying to prove, of course. Actually, my teacher once said that he considered giving bonus marks to a student that used lhopital's rule in an exam so im quite sure you can quote that kinda stuff. pretty sure Ex2 wouldnt limit you like that.
but im not really qualified to say this and perhaps someone will correct me

 

[RealiseNothing]

really? im pretty sure you can quote that. you cant quote it if it is indeed what you are trying to prove, of course. Actually, my teacher once said that he considered giving bonus marks to a student that used lhopital's rule in an exam so im quite sure you can quote that kinda stuff. pretty sure Ex2 wouldnt limit you like that.
but im not really qualified to say this and perhaps someone will correct me

Quote something like L'Hopital's and you'll get 0.

 

[Trebla]

Read the syllabus document. General rule of thumb is if the formula isn't there then you cannot quote it.

 

[Nailgun]

1) My teacher said its not assumed knowledge and quoting it will be like using Le hopsin's rule or wotever its called...

soz was lurking but couldn't resist