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#1 2017-03-18 05:45:46

CIV
Member
Registered: 2014-11-09
Posts: 66

Mean Value Theorem

The book I'm using says that the Mean Vaule Theorem does not apply with this function:

Why is this? It's continuous and differentiable right?

Using the MVT formula I get:

Then I solve for it's derivative and get:

Then I determine where the slope is 1/2:

I don't understand. The book says as the answer is "Does not apply".

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#2 2017-03-18 05:56:24

zetafunc
Moderator
Registered: 2014-05-21
Posts: 1,979
Website

Re: Mean Value Theorem

CIV wrote:

The book I'm using says that the Mean Vaule Theorem does not apply with this function:

Why is this? It's continuous and differentiable right?

It is not continuous on [-8,8], because your function isn't continuous at 0 (and therefore won't be continous in any neighbourhood of 0). It is also not differentiable at 0.

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#3 2017-03-18 06:09:34

CIV
Member
Registered: 2014-11-09
Posts: 66

Re: Mean Value Theorem

I made a mistake.... darn it. Sorry.

It's:

It's continuous and I just figured out that it's not differentiable at 0. The slope at zero is undefined.

I always make mistakes like that when posting online. Usually when I post online my brain is hurting from trying to figure things out.

Last edited by CIV (2017-03-18 06:10:22)

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#4 2017-03-18 06:21:00

zetafunc
Moderator
Registered: 2014-05-21
Posts: 1,979
Website

Re: Mean Value Theorem

Often, posting about a problem forces you to reason through your own work again and help you spot any mistakes in your derivations. That's the magic of the Help Me forum!

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