math mean value theorem
posted by manny on .
Hi I am having some trouble with these few quetions I would appreciate some help so that I can understand them better.
1) What, if anything, does the mean value theorem guarantee for the given function on this interval?
a) f(x) = x^2  2x + 5 on [1,4]
I am a bit uncertain on how to answer this, I started out with
f '(c) = f(b)  f(a) / ba = 13  4 / 3 = 9 / 3 = 3.
Then I plugged in 3 for f(x) and got 8.
Does this mean that (3,8) is a critical point?
b) g(x) = 8 / [(x2)^2] on [1,4]
I am sure this one needs a similiar approach to the last
Lastly:
What values c (if any) are predictable by the mean value theorem for the function f(x) = (x2)^3 on the interval [0,2]?
I proceeded similiarly here like the last question.
f '(c) turned out to be 4, and f(4) was 8.
I would greatly appreciate some help, since I am having trouble understanding the question and what it is asking.
Thanks!

f '(c) = f(b)  f(a) / ba = 13  4 / 3 = 9 / 3 = 3.
There exists a point c in the interval [1,4] such that f'(c) = 3 
ok thanks

4+20=46

verify that the function to satisfies roller's theorem of f /x/=x3x+2x+5 [0,2].