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) / b-a = 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 / [(x-2)^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) = (x-2)^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!
4 answers
There exists a point c in the interval [1,4] such that f'(c) = 3