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It means any x will be the integer below it, for example f(1.999)=1

f(-3.2222)=-4

but they want me to get the derivative of it and graph the derivative..

and they get a really weird graph, where it is unknown on every whole number

|dw:1328116598663:dw|The graph of f(x)=[[x]] looks like

yes, but they want me to get the derivative, one second let me draw it

It's called the "greatest integer function"

It's not differentialiable at any integers because the graph is discontinuous at all integers

|dw:1328116744272:dw|

that is a bar drawing, but ya get the picture

Any the derivative everywhere else is 0

because they are horizontal lines

so.. the double brackets means that it is discontinuous at all integers?

no...the double brackets mean it's the greatest integer function

as you can see from my crude drawing, at every integer the graph is discontinous

they if it is "greatest integer" wouldn't ti still be an integer?

The greatest integer function means the greatest integer less than x

less than or equal to x

but x is a variable

yes...

But if you plug in any value for x, say 1.98271, f(x)=1

then if it = 1 then why is it not defined at one? and i am sorry I am not understanding this

The differential is not defined at 1, f(x)=[[x]] is defined

oh, now i get it, because we are getting the derative of it that is why it is 0

sorry, my mind just wasn't working on all 4 cylinders

i get it now

lol no problem

thx for your time