Question

what is the derivative of f(x)=llxll (those are greatest integer function brackets)

Answer 1

It's zero everywhere except at the integers, where it is not well-defined.

Answer 2

huh?
could you explain that please?

Answer 3

If you plot the greatest integer function it looks like this:

Everywhere there is a flat piece, the derivative is equal to zero, but at the breaks, the derivative is not well-defined.

Answer 4

so i need to find the critical points if the function is at [-2,2]. so f'(x)= ll 1 ll =0 so the critical point(s), i don;t know how to find that if there is no x for the -2 and 2 to be plugged in

Answer 5

i need to find the absolute extrema on a closed interval

Answer 6

I mean, it's quite clear that the extrema of this function over an interval are going to be at the endpoints, isn't it?

Answer 7

The whole procedure of "Find the derivative, set it equal to zero, find the critical points, find the extrema" goes out the window if the function isn't differentiable over the whole interval, which it isn't.

Answer 8

ok, thank you, i think

Answer 9

You're welcome, I think.