mathematics , calculus

verify that the function satisfies the hypotheses of the mean value theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle’s Theorem.

f(x)=√x-1/3 x,[0,9]

  1. 👍
  2. 👎
  3. 👁
  1. (f(9)-f(0))/9 = (0-0)/9 = 0
    Since f(0) = f(9) we can apply Rolle's Theorem.

    f'(x) = 1/(2√x) - 1/3
    So, look for some value x=c such that f'(c) = 0
    1/(2√c) = 1/3
    2√c = 3
    c = 9/4

    1. 👍
    2. 👎

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. Please check my Calculus

    1. Find all critical values for f(x)=(9-x^2)^⅗ A. 0 B. 3 C. -3,3 D. -3, 0, 3 E. none of these I got D. I found the derivative and solved for critical numbers. 2. Find all intervals on which the graph of f(x)=(x-1)/(x+3) is

  3. 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 ( −

  4. 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. 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

  2. math

    Determine if the Mean Value Theorem for Integrals applies to the function f of x equals the square root of x on the interval [0, 4]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem.

  3. Calculus

    1. Construct a function f(x) that satisfies the following conditions: I. Its domain is all real numbers. II. It has no maximum and no minimum on the interval [ 1,3] . III. It satisfies f(1) = 1 and f(3) = –1, but there does not

  4. 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)

  1. 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

  2. Calculus

    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) =

  3. AP CALC

    Find the POSITIVE value of x that satisfies the mean value theorem for f(x)=sin(x) on the closed interval [-3pi/2, 3pi/2]. please help I have no idea how to solve this problem

  4. 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 −

You can view more similar questions or ask a new question.