A function f is defined by:

where and [.] denotes the greatest integer function.

Discuss the continuity and differentiability of at

Printable View

- Apr 28th 2009, 12:11 AMfardeen_genDiscuss continuity and differentiability of f(x)?
A function f is defined by:

where and [.] denotes the greatest integer function.

Discuss the continuity and differentiability of at - Apr 28th 2009, 12:37 AMredsoxfan325
- Apr 28th 2009, 11:04 AMredsoxfan325
It follows that is not diffrentiable at , because it is not continuous.

At , we have: .

Looking at and assuming (I think this is OK to assume because we want ), we know that and , so as becomes less than , we have:

Looking at and assuming , we know that , and we have:

So I think is differentiable at , and furthermore that and the tangent line is .

I'm only moderately confident about this response.