Mean Value Theorem

[nikchic5]

9
Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers that satisfy the conclusion of the Mean Value Theorem.

f(x)= 3(x^2) + 8x + 2 [ -3, 5 ]


If there is more than one answer, separate them by commas.



Thanks soooo much!

 

[ChaoticLlama]

Do you know what the mean value theorem is? It states that for a given function f(x) that is differentiable and continuous over the interval [a,b], there exists at least one point, (c,f(c)) such that the slope at (c,f(c)) is equal to the slope of the secant from (a,f(a)) to (b,f(b)).

http://en.wikipedia.org/wiki/Mean_value_theorem

Please post what you have tried so far to solve this problem.

 

[Matt]

Here you can find an example of the Mean Value Theorem in action.

 

[nikchic5]

Question...

Ok well I went to that website that I was told to get an example. And if I follow that then I get

F'(c) = - 1/169 and I don't see how that answers me question...sorry I need HELP! Thanks so much!

 

[stapel]

Re: Question...

I get F'(c) = - 1/169 and I don't see how that answers me question.

The point of the question was that you were supposed to find "c" so that F'(c) equalled [F(b) - F(a)]/(b - a). According to what you have posted (above), you have found some value of "c". What value are you using? How did you obtain it?

Please reply showing all of your steps, including finding the slope between the endpoints and finding the derivative.

Thank you.

Eliz.

 

[nikchic5]

This is what I got...

I did
f(5) - f(-3) / 5+3 which equals 14

And the derivative is 6x+8

But following the link to the website I plugged 14 into - 1 / (c-1)^2 and got -1/169.
Sorry I am really confused! Thanks for the help!

 

[stapel]

Re: This is what I got...

I did f(5) - f(-3) / 5+3 which equals 14 And the derivative is 6x+8

So now follow the rest of the instructions: Set the derivative formula equal to the slope, and solve for x (which is the "c" to which the Theorem refers).

I plugged 14 into - 1 / (c-1)^2 and got -1/169.

How does this relate to the exercise? Where did "-1/(c - 1)²" come from?

Thank you.

Eliz.

 

[nikchic5]

Ok

Ok when I set the derivative euqal to the slop I get x=1. Where do I go from there?

Also the equation with c came from the website that the other person told me to go to . Thanks so much for taking your time with me!

 

[pka]

Re: Ok

Ok when I set the derivative euqal to the slop I get x=1. Where do I go from there?

You don't go anywhere. That is the answer: c=1.

 

[nikchic5]

So...

So there is only one anser and it is 1?
Thanks so much!

 

[ChaoticLlama]

Re: So...

So there is only one anser and it is 1?
Thanks so much!

there may be more than one solution. Look at the Wikipedia article that I linked for a visual.

I think you should read the whole article very carefully. You seem to need the help.