could you help me with understanding the MATH of this proble

[Kristy]

Could you help me understand where the answers for number 7 come from?
Use the graphs of f to estimate the values of c that satisfy te conclusion of the Mean Value Theorem for the interval [ 0, 8 ].


[There is an image of a graph I am trying to copy and past but it won’t let me.] How do I get that function to work. It says IMG and I do paste but it doesn't work.

[img=http://img27.picoodle.com/img/img27/9/7/12/f_weirdcalculm_d7c92b1.jpg]

My work for number 7 (using the answers from the back of the book):
\(\displaystyle \frac{F[8]-F[0]}{8-0}\) = \(\displaystyle \frac{6-4}{8-0}\)= \(\displaystyle \frac{2}{8}\) =\(\displaystyle \frac{1}{4}\)

1. f is continuous on [a,b]
2. f’ is differeintiable
3. Then there exists a paint between 0 and 8 where
f’[c] = 1 /4
Positive inflection points on f’(x)?? (no idea what this means.)
C = 0.8 and 3.1 and 4.4 and 6.1
Those are c values that satisfy conclusion of MVT

I'm really confused by this and just copied the answer but do not understand it. I understand the continuous part, but how do you know the derivative is differentiable? And the c part totally mixes me up!

Edit: don't understand this graph ANDcan't get the image to showupI changed the title.

 

[stapel]

There is an image of a graph I am trying to copy and past but it won’t let me. How do I get that function to work. It says IMG and I do paste but it doesn't work.

To learn how to post images, please review the relevant FAQ item, and follow the instructions posted. there.

Thank you.

Eliz.

 

[Kristy]

To learn how to post images, please review the relevant FAQ item, and follow the instructions posted there.

I'm sorry, I read this but still do not know how to do this--?

 

[morson]

 

[stapel]

I'm sorry, I read this but still do not know how to do this--?

Just do what the instructions say:

i) Upload the image somewhere web-viewable (such as ImageBucket or your own web page), noting the exact URL, such as:

. . . . .http://img27.picoodle.com/img/img27/9/7/12/f_weirdcalculm_d7c92b1.jpg

ii) Post a direct link to the image, putting "IMG" tags on either side of it, so the image link:

. . . . .

...displays:

. . . . .

Please clarify where in this process you are getting stuck...? Thank you!

Eliz.

 

[Kristy]

Please clarify where in this process you are getting stuck...? Thank you!

Eliz.

Did I do something wrong? What I was stuck on was I had never even heard of how to create an image saved on a www page unless you had your own web page. I don't. So I figured out by looking at some other posts what people did and found imageshack.com and somehow mine ended up with a different www address, I tried copyin and pasting every version of it they gave me, and was only able to get a hyperlink to work. Everything else was just text. I don't know if you saw it while I was trying. There were many lines and nothing worked. Thanks to all the people who made the picture show up. I''m going to look at yours by quoting it to learn. I dono't rerally know what I was doing wrong other than that I did not get it to show itself up.


Anyway, now hopefully I will be able to do that, what I am referring to that I am getting stuck is:

How did I know to use 0 and 8? Was that where the problem started and ended on the x axis? Then I guess I'm trying to find the slope between the points at 0 and 8? I just copied those other thigns as conditions from the Rolle's theorem. It doesn't make sense to me why those conditions mean that somewhere the tangent line is the same as the line connecting thee 0 and the 8.

And I just have no idea what it was referring to about positive inflection points, I'm trying to undrestand that concept and it seems like it is where the derivative goes from being there to being gone or back again? [/tex]