math mean value theorem
posted by manny .
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].
Respond to this Question
Similar Questions

calculus
Let f(x) = (x+1)/(x1). Show that there are no vlue of c such that f(2)f(0) =f'(c)(20). Why does this not contradict the Mean Value Theorem? 
CALCULUS!
suppose that 3 <_ f prime of x <_ 5, for all values x. show that 18<_ f(8)f(2) <_ 30 <_ signs mean less or equal to... im supposed to apply mean value theorem or rolle's theorem... i don't understand neither so i cant … 
Caluclus
[Mean Value Theorem] f(x)=3x^3  4x^2  2x 3 on the closed interval [0,8]. Find the smallest value of c that satisfies the conclusion of the Mean Value Theorem for this function defined on the given interval. I got 8  sqrt(5696) … 
calculus
verify that the function satisfies the hypothesis of the mean value theorem on the given interval. then find all numbers c that satisfy the conclusion of the mean value theorem. f(x) = x/(x+2) , [1,4] 
math
verify that the function satisfies the hypothesis of the mean value theorem on the given interval. then find all numbers c that satisfy the conclusion of the mean value theorem. f(x) = x/(x+2) , [1,4] 
Math  Calculus
Show that the equation x^315x+c=0 has at most one root in the interval [2,2]. Perhaps Rolle's Theorem, Mean Value Theorem, or Intermediate Value Theorem hold clues? 
Calculus
Verify the hypothesis of the mean value theorem for each function below defined on the indicated interval. Then find the value “C” referred to by the theorem. Q1a) h(x)=√(x+1 ) [3,8] Q1b) K(x)=(x1)/(x=1) [0,4] Q1c) Explain … 
math
verify that the function satisfies the hypotheses of the mean values theorem on the given interval. then find all numbers c in the given interval that satisfy the conclusion of the mean value theorem. f(x)=2x/x4 [0,3] 
Calculus
Given f(x) = 1/x, find all c in the interval [3, ½] that satisfies the Mean Value Theorem. A. c= sqrt(3/2) B. c= +or sqrt(3/2) C. The Mean Value Theorem doesn’t apply because f is not continuous at x=0 D. The Mean Value Theorem … 
Calculus
show that ((x − 1)/x) <( ln x) < (x − 1) for all x>1 Hint: try to apply the Mean Value Theorem to the functions f(x) = lnx and g(x) = xlnx. I'm having trouble applying the mean value theorem