# Homework Help: Verifying the mean value theorum for absolute value function

1. Mar 18, 2008

### silicon_hobo

1. The problem statement, all variables and given/known data
a) Find the average value of the function $$f(x)=|x-1|$$ over [0,2].
b)Verify the mean value theorum for integrals for the function and interval in part (a).

2. Relevant equations
mean value theorum for integrals: $$\int_a^{b} f(x)dx=f(c)(b-a)$$

mean value theorum for differentials: $$f\prime(c)=\frac{f(b)-f(a)}{b-a}$$

3. The attempt at a solution
http://www.mcp-server.com/~lush/shillmud/int1.10.JPG
I believe part (b) is asking me to use the differential theorum to prove what has been found in part (a) but I'm rarely sure what to do when asked to 'verify' or 'prove'. Am I on the right track in my attempt to use the differential mvt to verify what I have found with the integral mvt in the first part? I know something's not right because the derivative of |x-1| is going to be either 1 or -1 at all times yet I've got an answer of 0 in part (b). Some clarification on how these theories work with regards to this problem would be greatly appreciated. Thanks for reading.

Last edited: Mar 19, 2008
2. Mar 19, 2008

### silicon_hobo

Bump. I'm still stumped on this one.

3. Jun 20, 2010