Question

Mean Value Therorem
f(x)=absolute value(x-1)
from -1 to 4

Answer 1

[f(b)-f(a)]/ (a-b)

Answer 2

f'(c)= f(4)-f(-1)/4-(-1)

Answer 3

hint: check the hypothesis of the mean value theorem before you try to apply it

Answer 4

f(4)=3
f(-1)=2

Answer 5

mean value theorem says nothing if the conditions of the theorem are not met

Answer 6

Yeah, absolute value is not necessarily a good function to apply it to

Answer 7

I have no choice, it is my assigned problem. I can not pick and choose what to solve.

Answer 8

anyways, doesn't one point in the interval have to have a derivative?

Answer 9

we know it fails at the corner but are they not other places we can find a derivative?

Answer 10

at every point in the interval the function need to be differentiable

Answer 11

ok let me spell it out
the hypothesis of the mean value theorem is that f is differentiable on the open interval (a,b) and continuous on the closed interval [a,b]

\[|x-1|\] is not differentiable at x =1 so mean value theorem says nothing about this function

Answer 12

well I do have a part b that states if so, that should tell me that the mean value theorem can fail this function.
Gotta love those absolute functions. Thanks :)

Answer 13

I am done with calculus tonight
Good night AccessDenied