anonymous
  • anonymous
f(x)=[[x]] what does the double bracket mean?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
It means any x will be the integer below it, for example f(1.999)=1
anonymous
  • anonymous
f(-3.2222)=-4
anonymous
  • anonymous
but they want me to get the derivative of it and graph the derivative..

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anonymous
  • anonymous
and they get a really weird graph, where it is unknown on every whole number
anonymous
  • anonymous
|dw:1328116598663:dw|The graph of f(x)=[[x]] looks like
anonymous
  • anonymous
yes, but they want me to get the derivative, one second let me draw it
anonymous
  • anonymous
It's called the "greatest integer function"
anonymous
  • anonymous
It's not differentialiable at any integers because the graph is discontinuous at all integers
anonymous
  • anonymous
|dw:1328116744272:dw|
anonymous
  • anonymous
that is a bar drawing, but ya get the picture
anonymous
  • anonymous
Any the derivative everywhere else is 0
anonymous
  • anonymous
because they are horizontal lines
anonymous
  • anonymous
so.. the double brackets means that it is discontinuous at all integers?
anonymous
  • anonymous
no...the double brackets mean it's the greatest integer function
anonymous
  • anonymous
as you can see from my crude drawing, at every integer the graph is discontinous
anonymous
  • anonymous
they if it is "greatest integer" wouldn't ti still be an integer?
anonymous
  • anonymous
The greatest integer function means the greatest integer less than x
anonymous
  • anonymous
less than or equal to x
anonymous
  • anonymous
but x is a variable
anonymous
  • anonymous
yes...
anonymous
  • anonymous
But if you plug in any value for x, say 1.98271, f(x)=1
anonymous
  • anonymous
then if it = 1 then why is it not defined at one? and i am sorry I am not understanding this
anonymous
  • anonymous
The differential is not defined at 1, f(x)=[[x]] is defined
anonymous
  • anonymous
oh, now i get it, because we are getting the derative of it that is why it is 0
anonymous
  • anonymous
sorry, my mind just wasn't working on all 4 cylinders
anonymous
  • anonymous
i get it now
anonymous
  • anonymous
lol no problem
anonymous
  • anonymous
thx for your time

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