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 commaseparated list.) f(x) = sqrt(x) − (1/9)x, [0,
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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 function f on the closed

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 xcoordinates of the point(s) guaranteed to exist by the theorem. a) No, the theorem does not apply b) Yes, x=16/9 c) Yes, x=1/4

Calculus
Determine if the Mean Value Theorem for Integrals applies to the function f(x)=2x^2 on the interval [0,√2). If so, find the xcoordinates of the point(s) guaranteed by the theorem a) No, the Mean Value Theorem for Integrals does not apply b) Yes, x=4/3

CalculusMath
The ordering and transportation cost C for components used in a manufacturing process is approximated by the function below, where C is measured in thousands of dollars and x is the order size in hundreds. C(x) = 12((1/x)+((x)/(x+3))) (a) Verify that C(2)

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 '(c) = 0. (Enter your

Math help please
In this problem you will use Rolle's theorem to determine whether it is possible for the function f(x) = 8 x^{7} + 7 x  13 to have two or more real roots (or, equivalently, whether the graph of y = f(x) crosses the xaxis two or more times). Suppose that

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 , 4 ) such that f ' ( c

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 commaseparated list.) f(x) = 5 − 6x + 3x2, [0, 2] can

Math11
Hello, I don't know how to do this, please help. Thank you. 1).Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 5x2 − 3x + 2, [0, 2] Yes, it does not matter if f is continuous or differentiable, every

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 exist a c between 1 and 3

calculus
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = x3 + x − 9, [0, 2]

CALCULUS!
Consider the function f(x)=4x^3–2x on the interval [–2,2]. Find the average or mean slope of the function on this interval. __14__ By the Mean Value Theorem, we know there exists at least one c in the open interval (–2,2) such that f(c) is equal to

calculus
Find the values of c that satisfy the Mean Value Theorem for f(x)=6/x3 on the interval [1,2]. Is it no value of c in that interval because the function is not continuous on that interval???

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 commaseparated list.) f(x) = sqrt(x) − (1/9)x, [0, 81] c=?

Calculus
Rolle's theorem cannot be applied t the function f(x)= ln(x+2) on the interval [1,2] because a) f is not differentiable on the interval [1,2] b) f(1)≠ f(2) c) All of these d) Rolle's theorem can be applied to f(x)= ln(x+2) on the interval [1,2]

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? ...Other than simply using my TI84, I have no idea how to accomplish this.

Calculus
1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2]. 2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[4,2]. If Rolle's Theorem can be applied, find all values of c

calculus
f(x) = ln x, [1, 6] If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a commaseparated list. If it does not satisfy the hypotheses, enter DNE).

Calculus Help Please!!!
does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 2x^2 − 5x + 1, [0, 2] If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a

Calculus
By applying Rolle's theorem, check whether it is possible that the function f(x)=x^5+x−5 has two real roots. Answer: (input possible or impossible ) Your reason is that if f(x) has two real roots then by Rolle's theorem: f′(x) must be (input a number

Calculus
Using the function y= 1/3x^3 a) Verify that the function satisfies the hypotheses of the Mean Value Theorem on the interval [3,3]. b) Then find all numbers c that satisfy the conclusion of the Mean Value Theorem.

calculus help
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)= ln(x) , [1,6] If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a commaseparated

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]

Calculus
The function defined below satisfies the Mean Value Theorem on the given interval. Find the value of c in the interval (1, 2) where f'(c)=(f(b)  f(a))/(b  a). f(x) = 1.5x1 + 1.1 , [1, 2] Round your answer to two decimal places.

calculus
Find the values of c that satisfy the Mean Value Theorem for f(x)=6/x3 on the interval [1,2]. Is it no value of c in that interval because the function is not continuous on that interval???

calculus
Consider the function f(x) = 33 x^{2/3} on the interval [ 1 , 1 ]. Which of the three hypotheses of Rolle's Theorem fails for this function on the inverval? (a) f(x) is continuous on [1,1]. (b) f(x) is differentiable on (1,1). (c) f(1)=f(1). Answer:(

Calculus
Verify the conditions for Rolle's Theorem for the function f(x)=x^2/(8x15) on the interval [3,5] and find c in this interval such that f'(c)=0 I verified that f(a)=f(b) and calculated f'(x)= (8x^2 30x)/64x^2 240x +225) But I'm having trouble finding c

Calculus
Rolle's theorem cannot be applied t the function f(x)= ln(x+2) on the interval [1,2] because a) f is not differentiable on the interval [1,2] b) f(1)≠ f(2) c) All of these d) Rolle's theorem can be applied to f(x)= ln(x+2) on the interval [1,2]

ap calc
Find the value of c which satisfies Rolle's Theorem for the function f(x)=sin(x^2)on (0, ãpi).

Calculus
Use the graph of f(x)=x^2/(x^24) to determine on which of the following intervals Rolle’s Theorem applies. A. [0, 3] B. [3, 3] C. [3/2, 3/2] D. [2, 2] E. none of these I know what the Rolle's Theorem is but I'm unsure on how you know if the function

calc
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 commaseparated list.) f(x) = x^3 − x^2 − 12x + 8, [0, 4]

Calculus
verify that the function satisfies the three hypotheses of rolle's theoreom on the given interval then find all numbers c that satisfy the conclusion of rolle's theorem. 1) 512x+3x^2 [1,3]

calc
verify that g(x)=3x sqrt(x5) satisfies the condition of rolle's theorem on the interval [0,5]. Find all numbers c that satisfies rolles theorem.

Math
The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (0,1) where f'(c)=0. f(x) = x^3  2x^2 + x, [0, 1] Round your answer to two decimal places.

Calculus Help Please!!!
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 2x^2 − 5x + 1, [0, 2] If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a

Calculus
Verify that the hypotheses of the MeanValue Theorem are satisfied for f(x) = √(16x^2 ) on the interval [4,1] and find all values of C in this interval that satisfy the conclusion of the theorem.

Calculus
Determine if Rolle's Theorem applies to the given function f(x)=2 cos(x) on [0, pi]. If so, find all numbers c on the interval that satisfy the theorem.

Calculus
For f(x)=x^2/3(x^24) on [2,2] the "c" value that satisfies the Rolle's Theorem is A. 0 B. 2 C. +or2 D. There is no value for c because f(0) does not exist E. There is no value for c because f(x) is not differentiable on (2,2)

ap calc
Find the value of c which satisfies Mean Value Theorem for the function f(x)=sin(x) on the closed interval (3ð/2,3ð/2).

calculus
find all the numbers c that satisfy the conclusion of rolle's theorem.... f(x)= cos 2x on the interval [0,3]

math mean value theorem
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

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 doesn’t apply

Please check my Calculus
1. Which of the following describes the behavior of f(x)=x^3x A. Relative maximum: x=0 B. Relative maximum: x=(1/sqrt(3)); Relative minimum: x=(1/sqrt(3)) C. Relative maximum: x=(1/sqrt(3)); Relative minimum: x=(1/sqrt(3)) D. Relative minimum: x=0 E.

calc
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. f(x)= x sqrt(x+21) , [21,0] If there is more than one solution separate your answers

URGENT!! PLEASE Calc
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. f(x)=sin4pix , [1/2,1/2] Well according to Rolle's Theorem, it has to be continuous

math
Verify that the function f(x)=x^36x^2+8x+4 satisfies the three hypotheses of Rolle's Theorem on the given interval [0,4]. Then find all numbers c that satisfy the conclusion of Rolle's Theorem

Calculus 1
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 commaseparated list.) f(x) = x^3−x^2−20x + 7, [0, 5]

math
Question Part Points Submissions Used 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 commaseparated list.)

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)=√x1/3 x,[0,9]

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]

Math
The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (0,1) where f'(c)=0. f(x) = x3  2x2 + x, [0, 1] Round your answer to two decimal places.

calculus
Rolle's theorem cannot be applied to the function f(x) = x1/3 on the interval [–1, 1] because Answer Choices: f is not differentiable on the interval [–1, 1] f(–1) ≠ f(1) f is not differentiable on the interval [–1, 1] and f(–1) ≠ f(1)

AP Calc
Find the value of c which satisfies Rolle’s Theorem for the function f(x)=sin(x²) on (0,√π).

AP Calc
Find the value of c which satisfies Rolle’s Theorem for the function f(x)=sin(x²) on (0,√π).

calculus
Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = x^2/3 − 2, [−8, 8] 1) Yes, Rolle's Theorem can be applied. 2)No, because f is not continuous on the closed interval [a, b]. 3)No,

Calculus
The function f(x) = 5x sqrt x+2 satisfies the hypotheses of the Mean Value Theorem on the interval [0,2]. Find all values of c that satisfy the conclusion of the theorem. How would you use the MVT? I tried taking the derivative, in which resulted in

maths need help
using the interval [0,2pi] and f(x) = sinx + cosx, obtain c £ (0,2pi) that satisfies the conclusion of Rolle's theorem where £ mean element of and C means number show step

Calculus
1. Determine whether Rolle's Theorem applied to the function f(x)=((x6)(x+4))/(x+7)^2 on the closed interval[4,6]. If Rolle's Theorem can be applied, find all numbers of c in the open interval (4,6) such that f'(c)=0. 2. Determine whether the Mean Value

mean value theorem
Show that the function f(x)=1x, [1,1] does not satisfy the hypotheses of the mean value theorem on the given interval. Also how do I graph the function together with the line through the points A(a,f(a)) and B(b,f(b)). Also how do I find values of c in

Calculus
The ordering and transportation cost C for components used in a manufacturing process is approximated by C(x) = 20 (1/x + x/ (x+3)) where C is measured in thousands of dollars and x is the order size in hundreds. (a) Verify that C(3) = C(6). (b) According

Calculus
Let f(x)=5x2+5x−12. Answer the following questions.Find the average slope of the function f on the interval [−1,1].Verify the Mean Value Theorem by finding a number c in (−1,1) such that f′(c)=m¯¯¯.

Calculus
Hello. I have a few questions from my study guide, that I need to know to study for my test. 1) x^(2/3)*((5/2)(x) a) determine the ordered pairs of the local extrema of the function. Use the second derivative test. B) determine the ordered pairs of all

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.

Calc, Mean Value Theorem
Consider the function : 3x^3  2x^2  4x + 1 Find the average slope of this function on the interval. By the Mean Value Theorem, we know there exists a "c" in the open interval (2,3) such that f'(c) is equal to this mean slope. Find the two values of "c"

calc
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. f(x)=sin4pix , [1/2,1/2] Well according to Rolle's Theorem, it has to be continuous

calculus
Consider the function f(x) = x^33x^2+2x18 on the interval [ 0 , 2 ]. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval: f(x) is ___on[0,2] f(x) is ___ on (0,2) and f(0)=f(2)=____ then by rolle's theorem, there

calculus
Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the three hypotheses of Rolle’s theorem on the interval [0,3]. Then find the values of c on the interval [0,3] that are guaranteed by Rolle’s theorem. Give your answer as a set of values, e.g.,

calculus
Verify that the hypotheses of Rolle’s Theorem are satisfied for f(x)=6cosx on the interval [9pi/2,11pi/2] and find all values of c in this interval that satisfy the conclusion of the theorem.

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 values theorem f(x)= 2x/x4 [0,3]

Calculus
The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (0,1) where f'(c)=0. f(x) = x3  2x2 + x, [0, 1] Round your answer to two decimal places.

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]

calculus
Verify that the hypotheses of the MeanValue 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^23x; [2,6]

math  very urgent !
Verify that f(x) = x^3 − 2x + 6 satisfies the hypothesis of the MeanValue Theorem over the interval [2, 3] and find all values of C that satisfy the conclusion of the theorem.

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) / 18 = 3.748436059 but

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 the difference between the

calculus
Rolle's theorem cannot be applied to the function f(x) = x^1/3 on the interval [–1, 1] because... f is not differentiable on the interval [–1, 1] f(–1) ≠ f(1) f is not differentiable on the interval [–1, 1] and f(–1) ≠ f(1) Rolle's theorem

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 I.

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? ...Other than simply using my TI84, I have no idea how to accomplish this.

Please check my Calculus
1. Find the value(s) of c guaranteed by Rolle’s Theorem for f(x)=x^2+3x on [0, 2] A. c=3/2 B. c=0, 3 C. Rolle’s Theorem doesn’t apply as f is not continuous on [0, 2] D. Rolle’s Theorem doesn’t apply as f(0) does not equal f(2) E. None of these

Calc
This problem is really weird. I have to explain why MVT applies for f(x)=2sinxsin2x on the closed interval 7pi,8pi and then determine all values of c in the interval (7pi,8pi) that satisfies the conclusion of the theorem. However, the condition of MVT is

CALCULUS
Determine whether F satisfies the hypotheses of the mean value theorem on [a,b], and if so, find all numbers c in (a,b). f(x)=X^2/3 [8,8] why this answer is f is not differantible?

Mathematics
use rolle's theorem to show that the equation 7x^69x^2+2=0 has at least one solution in the interval (0,1)

Calculus
Show that Rolle's Theorem applies to the given function for the given values of x: x=1 and x=4 for f(x)=3xx^2+2.

Calculus
Show that Rolle's Theorem applies to the given function for ht eg oven values of x: x=1 and x=4 for f(x)=3xx^2+2

calculus
Consider the function f(x)=3x^2 – 5x on the interval [4,4]. Find the average slope of the function on this interval. By the mean value theorem, we know there exists at least one c in the open interval (4,4) such that f’(c) is equal to this mean

calculus
Consider the function f(x)=–3x3–1x2+1x+1Find the average slope of this function on the interval (–2–1). By the Mean Value Theorem, we know there exists a c in the open interval (–2–1) such that f(c) is equal to this mean slope. Find the value

calculus
verify the Intermediate Value Theorem if F(x)=squre root of x+1 and the interval is [3,24].

CALCULUS!
suppose that 3

calculus
Verify the means value theorem holds on the interval shown. Then, find the value c such that f'(c)=(f(b)f(a))/(ba) a. f(x)= x1/x on [1,3] b.f(x)=x^3=x4 on [2,3] c. f(x)= x^3 on [1,2] d. f(x)= Sqr. root of x on [0,4]

calc
Verify that the function satisfies the three hypotheses of Rolle's Therorem on the given interval. Then find all numbers c that satisfy the conclusiton of Rolle's Theorem. f(x)= x*sqrt(x+6) [6,0] f is continuous and differential f(6) =6*sqrt(6+6) =0

Calculus
The function defined below satisfies Rolle's Theorem on the given interval. Find the value of c in the interval (3, 2) where f'(c)=0. f(x) = x + 6x1 , [3, 2] Round your answer to two decimal places.

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 and found out that

Calculus
Show that the function f(x)= x^(3) +3/(x^2) +2 has exactly one zero on the interval (infinity, 0). So far this is what I have: 0=x^3 + 3/(x^2) +2 2= (1/x^2)(x^5 + 3) 2x^2= x^5 +3 But now I'm stuck. I also am not sure if this is how I'm supposed to be

math
Verify that f(x) = x^3 − 2x + 6 satisfies the hypothesis of the MeanValue Theorem over the interval [2, 3] and find all values of C that satisfy the conclusion of the theorem.

Math
Let f(x) = 2x + 1 − sin(x), how many roots does f(x) have in the interval [−π, π]? Use the next steps to prove that it has only one root. a) Use the Intermediate Value Theorem to show that f(x) has at least one root. (b) Explain why f(x) is

Calc 1
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)=x^3+x4 [0,2]

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).

calc
by applying rolle's theorem, check whether it is possible that the function f(x) = x^5 + x 17 has two real roots. your reason is that if f(x) has two real roots then by rolle's theorem, f'(x) must be equal to what at certain value of x between these two

calculus
Verify that the Intermediate Value theorem applies to the indicated interval and find the value of c guaranteed by the theorem. f(x) = x^2  6x + 8, [0,3], f(c) = 0 I have no idea how to use the theorem :(

Math
17) Consider the function f(x)=3x3−3x2+4x+2 Find the average slope of this function on the interval (−3,5). By the Mean Value Theorem, we know there exists a c in the open interval (−3,5) such that f′(c) is equal to this mean slope. Find the two