Thread: Mean value theorem

I have solved (a), but (b) is confusing and I don't know how to go about it...

Question:
(a) find the average value of the function; f(x)= abs(x-1) over [0,2]
answer= 1/2

(b) verify the mean value theorem for integrals for the function and interval in part (a)


Guidance in the right direction? Thank you!

cheers

Originally Posted by klooless

I have solved (a), but (b) is confusing and I don't know how to go about it...

Question:
(a) find the average value of the function; f(x)= abs(x-1) over [0,2]
answer= 1/2

(b) verify the mean value theorem for integrals for the function and interval in part (a)


Guidance in the right direction? Thank you!

cheers

Please give a complete statement of the mean Value Theorem For Integrals. Then please state exactly what part of this theorem you're having trouble verifying.

Thanks for responding mr fantastic,

the Mean Value Theorem for integrals is;

a∫b f(x) dx = f(c)(b-a)

what is unclear to me is what they mean by "verify". Do they want me to prove the theorum? if so, I used two equations for part (a), -x+1 and x-1 because of the abs value, how would I start proving it? through both equations?

thank you!

Since f(x) is continuous on [0,2], isn't it just asking to show that there exists a point c in [0,2] such that f(c) is equal to the mean value of the function over [0,2]?

Originally Posted by klooless

the Mean Value Theorem for integrals is;

a∫b f(x) dx = f(c)(b-a)

what is unclear to me is what they mean by "verify". Do they want me to prove the theorum? if so, I used two equations for part (a), -x+1 and x-1 because of the abs value, how would I start proving it? through both equations?

Not to be overly particular with you, but you haven't really stated the theorem, you've just stated the formula without the hypothesis. The hypothesis is the part of the theorem that tells you how the formula is used. Look at the hypothesis in your book, and you should find something like "For ... there exists a c...." So you will need to show that for the example they have given you, there exists a c...

Make sense?