Is the point x=3 a point of local minimum for this function?

[mathier]

Given the function f(x)=0 for x<=3 and f(x)=(x-3)^2 for x > 3.
Is the point x=3 a point of local for minimum for this function?
According to the widely accepted definition, it is.
Thank you!
mathier

 

[Steven G]

This is a help forum where we help students solve their problems. My advice to you is to read the posting guidelines so you know how to receive help.

 

[Harry_the_cat]

You say "Is the point x=3 a...".
First of all, x=3 is NOT a point at all. Do you mean the point (3, 0)?

 

[Dr.Peterson]

Given the function f(x)=0 for x<=3 and f(x)=(x-3)^2 for x > 3.
Is the point x=3 a point of local for minimum for this function?
According to the widely accepted definition, it is.
Thank you!
mathier

I would be interested in discussing this; it's a worthy question, once it's stated clearly.

If you want to have that serious discussion, please state the "widely accepted definition" you are using, as well as why you evidently question it. (I would too, though I will probably end up explaining why it makes sense after all.) The more you say about your thinking, the better the discussion will be.

 

[Harry_the_cat]

You know what I mean "ELITE MEMBER". Don't you by now?

Ex...cuse me??

“Then you should say what you mean,” the March Hare went on. “I do,” Alice hastily replied; “at least–at least I mean what I say–that's the same thing, you know.” “Not the same thing a bit!” said the Hatter.