Post a New Question

CALCULUS!

posted by .

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 do the question! please help!

  • CALCULUS! -

    If f'=3, then f=3x+C, so f(8)]=24+C, but C=2 if f'=3. So f(8)=26

    f(2)=8 by the same argument.

    then if f'x=3, f(8)-f(2)=26-8=>18

    You can make the same logic if f'=5, solve for C, then show that f(8)-f(2)<=30

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    Let f(x) = (x+1)/(x-1). Show that there are no vlue of c such that f(2)-f(0) =f'(c)(2-0). Why does this not contradict the Mean Value Theorem?
  2. calculus

    Referring to the Mean Value Theorem and Rolle's Theorem, how can I tell if f is continuous on the interval [a,b] and differentiable on (a,b).
  3. AP Calculus

    Show that the equation x^3 - 15x + c = o has exactly one real root. All I know is that it has something to do with the Mean Value Theorem/Rolle's Theorem.
  4. Math - Calculus

    Show that the equation x^3-15x+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?
  5. Math - Calculus

    Show that the equation x^3-15x+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?
  6. 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)=(x-1)/(x=1) [0,4] Q1c) Explain …
  7. Calculus

    Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(x)=0. f(x) = x^(2/3) - 1 [-8,8] I plugged in both values …
  8. math

    Suppose f(x) = x^3 on the interval [1, 4]. Use the Mean Value Theorem to find all values c in the open interval (1, 4) such that f'(c)= (f(4)-f(1))/4-1 c= square root of 7 c= cubed root of 21 c = 7 Mean Value Theorem does not apply
  9. 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 …
  10. 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

More Similar Questions

Post a New Question