calculus

Find the values of c that satisfy the Mean Value Theorem for f(x)=6/x-3 on the interval [-1,2].

Is it no value of c in that interval because the function is not continuous on that interval???

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. It is continuous between -1 and +3. The blow up is at x = 3.
    y = 6/(x-3)
    dy/dx = -6/(x-3)^2
    now slope from -1 to +2
    y(-1) = 6/-4 = -3/2
    y(2) = 6/-1 = -6
    delta x = 2+1 = 3
    so mean slope = (-6 + 3/2)/3 = -2 + 1/2 = -1.5
    now where does derivative = -1.5 ?
    -3/2 = -6/(x-3)^2
    (x-3)^2 = 4
    x-3 = +/- 2
    x = 5 or x = 1
    only x = 1 is on the interval from -1 to 2

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Let f be the function with f(0) = 1/ (pi)^2, f(2) = 1/(pi)^2, and the derivative given by f'(x) = (x+1)cos ((pi)(x)). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the

  2. Calculus

    Determine if the Mean Value Theorem for Integrals applies to the function f(x) = √x on the interval [0, 4]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem. a) No, the theorem does not apply b)

  3. Calculus

    Determine if the Mean Value Theorem for Integrals applies to the function f(x)=2-x^2 on the interval [0,√2). If so, find the x-coordinates of the point(s) guaranteed by the theorem a) No, the Mean Value Theorem for Integrals

  4. Calculus

    Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function. If there are multiple values, separate them with commas; enter N if there are no such values. f(x)= x^2-10x+3, [0,10]

  1. Calculus

    Which of the following functions does not satisfy the conditions of the Mean Value Theorem on the interval [-1, 1]? a. 5th root of x b. 2x arccosx c. x/(x - 3) d. sqrt(x + 1)

  2. math

    Find all the values of x in the interval [0,2π] that satisfy the equation: 8sin(2x)=8cos(x)

  3. Calc

    Given function f defined by f(x) = ( 1- x)³. What are all values of c, in the closed interval [0,3], that satisfy the conditions of the Mean Value Theorem?

  4. math

    Consider the function f ( x ) = 3x^3 − 3x on the interval [ − 4 , 4 ] . Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one c in the open interval ( −

  1. Calculus

    Find the exact values of x in the interval [0, 4π] that satisfy the equation sin x = -√2 / 2 (refer to y = sin x or y = cos x )

  2. math

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 5 −

  3. Math

    Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. (Select all that apply.) f (x) = sin(x), [0, 2π] If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f

  4. Calculus

    Consider f(x)=x^3-x over the interval [0,2]. Find all the values of C that satisfy the Mean Value Theorem (MVT)

View more similar questions or ask a new question.