AP CALCULUS

posted by .

Using the mean value theorem;
F'(x) = f(b)-f(a) / b-a

f(x)=x^2-8x+3; interval [-1,6]

  • AP CALCULUS -

    I assume you want to find c such that f'(c) = (f(6)-f(-1))/7

    nothing simpler:

    f'(x) = 2x-8
    f(6) = -9
    f(-1) = 12

    so, we want f'(c) = -21/7 = -3
    2x-8 = -3
    x = 5/2

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

    Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval, and find all values of c in that interval that satisfy the conclusion of the theorem. f(x)=x^2-3x; [-2,6]
  3. 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]
  4. Calculus

    Verify that the hypotheses of the Mean-Value Theorem are satisfied for f(x) = √(16-x^2 ) on the interval [-4,1] and find all values of C in this interval that satisfy the conclusion of the theorem.
  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. 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?
  7. 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 …
  8. calculus

    determine whether the mean value theorem can be applied to f on the closed interval [a,b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a,b) such that f(c) =f(b) - f(a) / b - a
  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

    Let f(x)=αx^2+βx+γ be a quadratic function, so α≠0, and let I=[a,b]. a) Check f satisfies the hypothesis of the Mean Value Theorem. b)Show that the number c ∈ (a,b) in the Mean Value Theorem is the midpoint of the interval …

More Similar Questions