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I understand that the local max of a function is the point at which the y value of the function is larger than the neighbouring y values of the function.

Say we're considering the local max at a of a function f(x). Does the function have to exist on both sides of a for (a,f(a)) to be a local max? (consider the same situation for a local min).

In short, if the fuction exists at [a, b] [tex]\epsilon[/tex][tex]\Re[/tex] only,

can there be a local max or min at (a, f(a)) or (b, f(b)) ?

My high school professor said that to have local extrema, the function should exist on either side of the point. However, I believe my University prof said that this is not the case.

Could someone please clarify as to which one is the case?

Thanks a ton!

Merry

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# Local max and min at a if lim f(x) approaching a does not exist

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