I have:

http://img12.imageshack.us/img12/6121/capturerhf.png

Is the function differentiable in (0,2)? If so, find its Tangent Plane.

Printable View

- Dec 13th 2011, 02:10 PMGIPCIs the following function differentiable?
I have:

http://img12.imageshack.us/img12/6121/capturerhf.png

Is the function differentiable in (0,2)? If so, find its Tangent Plane. - Dec 13th 2011, 03:43 PMFernandoRevillaRe: Is the following function differentiable?
We have , so

**if**is differentiable at the only possible differential is . Now, analyze if . - Dec 14th 2011, 04:08 AMGIPCRe: Is the following function differentiable?
I came to that lim term myself and that's where I kind of get stuck with all the epsilons. I can't draw a concrete conclusion from there if it is indeed 0 or just a small epsilon bigger than 0. That's what making this exercise difficult.

- Dec 14th 2011, 04:49 AMFernandoRevillaRe: Is the following function differentiable?
Use in a neighborhood of in the precise terms of the Taylor's formula.

- Dec 14th 2011, 07:35 AMGIPCRe: Is the following function differentiable?
I came to a conclusion that the function is indeed differentiable, but I have to show a strict rigorous proof.

How do I expand f to its Taylor Series?

And from there, how do I find the tangent plane? - Dec 14th 2011, 11:29 AMFernandoRevillaRe: Is the following function differentiable?
That is a correct conclusion.

Quote:

but I have to show a strict rigorous proof.

Quote:

How do I expand f to its Taylor Series?

Quote:

And from there, how do I find the tangent plane?

- Dec 14th 2011, 11:38 AMGIPCRe: Is the following function differentiable?
Sorry for the follow up questions. Even with the Taylor expansion, how do I use it in the lim term you prescribed earlier?

And also, after i prove differentiability, how do I find the appropriate P0 to plug into the formula for the tangent plane?

I'm sorry for asking pathetic questions :(