# Open Interval differention

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• August 14th 2011, 11:30 AM
rgjf1307
Open Interval differention
Does anyone know the answer to this??

Complete the definition:

A real function on an open Interval I is differentiable at x ∈ I if...

Is it to do with Rolle's Theorem, although that uses the property but doesnt actually define it?
• August 14th 2011, 01:58 PM
Plato
Re: Open Interval differention
The answer to your question could be in many forms.
$\lim _{h \to 0} \frac{{f(x + h) - f(x)}}{h}=f'(x)$ if the limit exists.

But there are others.
• August 14th 2011, 02:17 PM
rgjf1307
Re: Open Interval differention
Thank you for the response :)

What other forms could there be?
• August 14th 2011, 02:20 PM
Plato
Re: Open Interval differention
Quote:

Originally Posted by rgjf1307
Thank you for the response :)
What other forms could there be?

How does your text material define derivative?
That is all that is being asked there if you posted the question correctly.
• August 14th 2011, 02:28 PM
rgjf1307
Re: Open Interval differention
The narrative used is: A function f: I → ℝ on an open interval I is differentiable at x ∈ I if ...
• August 14th 2011, 02:33 PM
Plato
Re: Open Interval differention
Quote:

Originally Posted by rgjf1307
The narrative used is: A function f: I → ℝ on an open interval I is differentiable at x ∈ I if ...

That is exactly what you posted the first time.
Answer the question. Fill in the blank with the definition of a derivative as it appears in the text material.
• August 14th 2011, 02:44 PM
rgjf1307
Re: Open Interval differention
There is no definition in the text material so I guess I'll have to use the form you posted in your original reply!
• August 14th 2011, 02:57 PM
Plato
Re: Open Interval differention
Quote:

Originally Posted by rgjf1307
There is no definition in the text material so I guess I'll have to use the form you posted in your original reply!

If that is true, why are you being asked to do this?
This makes no sense whatsoever.
• August 14th 2011, 03:20 PM
rgjf1307
Re: Open Interval differention
OK, thanks for your help :)

On a similar note how would define a critical point of a differentiable function using the same notation?
• August 14th 2011, 03:36 PM
Plato
Re: Open Interval differention
Quote:

Originally Posted by rgjf1307
OK, thanks for your help :)

On a similar note how would define a critical point of a differentiable function using the same notation?

You did not bother to answer my question.
What is the purpose of this nonsense?
Why are you being asked to do these questions?
If you choose to ignore my request, then this is my last reply.
• August 14th 2011, 03:47 PM
rgjf1307
Re: Open Interval differention
I am being asked to do these questions because my lecturer told me to? Sorry man, didn't mean to ignore you, no hard feelings!
• August 14th 2011, 04:06 PM
Plato
Re: Open Interval differention
Quote:

Originally Posted by rgjf1307
I am being asked to do these questions because my lecturer told me to? Sorry man, didn't mean to ignore you, no hard feelings!

It seems to me that your lecturer is at best incompetent or at worst totally ignorant.
Report this person to your governing educational authority.
• August 14th 2011, 04:09 PM
rgjf1307
Re: Open Interval differention
Ok, I shall. But if possible could you first assist me on the last question? How would you define a critical point of a differentiable function using the same notation?

Thanks.
• August 14th 2011, 04:53 PM
HallsofIvy
Re: Open Interval differention
Are you taking a course on Calculus or not? How could you possibly answer a question about "differentiable" if you have never been given a definition of "differentiable"?

Okay, here's a similar question- is the function $f(x)= e^{x^2}- x$ "codsquafalic". I am not, of course, going to define "codsquafalic"!
• August 15th 2011, 03:45 PM
rgjf1307
Re: Open Interval differention
Hello there! Yes I am taking a course on Calculus and whilst I am aware of the process of differentiation from previous courses I have not been given a formal definition during this particular course.

The format Plato used earlier is along the lines of what I was hoping to achieve, I was just wondering how, using the same notation, would you define a critical point of a differentiable function?
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