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Find the mean value of the function f(x)=6-x on the closed interval [4,7]

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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 it's not right.

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
1. Determine whether Rolle's Theorem applied to the function f(x)=((x-6)(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 Theorem applied to ...

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 of c in the interval ...

math
Consider the function f(x)=–2x^3–3x^2+2x–2 Find the average slope of this function on the interval (2,6). ? By the Mean Value Theorem, we know there exists a c in the open interval (2,6) such that f'(c) is equal to this mean slope. Find the value of c in the interval ...

calculus
Consider the function f(x)=4sqrtx+5 on the interval [4,5]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (4,5) such that f'(c) is equal to this mean slope. For this problem, there is ...

math
Consider the function f(x)=2sqrtx+4 on the interval [2,8]. Find the average or mean slope of the function on this interval. ? By the Mean Value Theorem, we know there exists a c in the open interval (2,8) such that f'(c) is equal to this mean slope. For this problem, there is ...

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" in the interval which...

Calculus Please help!
Consider the function f(x)=4sqrt(x)+4 on the interval [2,5] . Find the average or mean slope of the function on this interval _______ <---A By the Mean Value Theorem, we know there exists a c in the open interval (2,5) such that f'(c) is equal to this mean slope. For this ...

calc
consider the function f(x)=x^3 - x^2 - 3x -2. find the average slope of this function on the interval (-2,3). 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 in the interval ...

calculus
Consider the function f(x)=6sqrt(x)+1 on the interval [3,5] . Find the average or mean slope of the function on this interval. I FOUND THIS: (6sqrt(5)-6sqrt(3))/2 By the Mean Value Theorem, we know there exists a c in the open interval (35) such that f(c) is equal to this mean...

Calculus Please help!
f(x) -2x^3+2x^2-3x+2 Find the average slope of this function on the interval (–3–1) ________ <--A By the Mean Value Theorem, we know there exists a c in the open interval (–3–1) such that f'(c) is equal to this mean slope. Find the value of c in the interval which ...

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

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 this mean slope. For ...

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???

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???

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 values ...

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?

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 slope. For this problem, ...

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 in the open interval...

Calculus
Find the average or mean slope of 2x^3 - 6x^2 - 90x +3 on the interval [-6,10]? By the Mean Value Theorem, we know there exists at least one c in the open interval ( -6 , 10 ) such that f'( c) is equal to this mean slope. ::>> I already found the mean slope of the ...

calc
Consider the function below. (Round the answers to two decimal places. f(x) = 2x tan(x) -p/2 < x < p/2 (a) Find the interval where the function is increasing. Find the interval where the function is decreasing. (b) Find the local minimum value. (c) Find the interval ...

Math
16) Consider the function f(x)=2x3−6x2−90x+5 on the interval [−6,7]. 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 (−6,7) such that f′(c) is ...

calculus
I have three questions I'm having a terrible time with: 1)Find, if possible, the absolute maximum value and where it occurs for f(x)=ln(xe^-x) on (0,infinity). 2)Find the value(s) of "c" guaranteed by the Mean Value Theorem for the function f(x)=ln(x^2) on the interval [1,e]. ...

Math
Consider the function f(x)=8(x^(1/2))+7 on the interval [1,5]. By the Mean Value Theorem, we know there exists a c in the open interval (1,5) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.

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) = 1.5x-1 + 1.1 , [1, 2] Round your answer to two decimal places.

mean value theorem
Show that the function f(x)=1-|x|, [-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 (a,b) that satisfy f...

Calculus
f'(x)=sqrt(x)*sin(x) The first derivative of the function f is given above. If f(0)=0, at which value of x does the function f attain it's minimum value on the closed interval [0,10]? I know the answer is 6.28, but I need steps as to why. Please and thank you.

Calc 1
Consider the function below. f(x) = (x^2)/(x−9)^2 (a) Find the vertical and horizontal asymptotes. x=? y=? (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval where the function is decreasing. (Enter your...

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

Calculus Help!!
Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x) = cos^-1(x/2 - 3), and the x axis. a. What is the area of the region R? b. Find the volume of the solid generated when region R is rotated about the x axis. c. Find all values c for f(x) and g(x) in the closed ...

Calculus HELP!!!
Here is the graph. h t t p : / /goo.gl/PTc2I (spaces added at the beginning so it could be added as a website) 1. Let g be the function given by g(x)=integrate from -4 to x f(t)dt. For each of g(-1), g'(-1), and g''(-1), find the value of state that it does not exist. 2. For ...

Calculus AB
The average value of a continuous function f(x) on the closed interval [3,7] is 12. Whats the value of ∫ from [3,7] f(x) dx?

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]

Calculus
The function f(x)=(x^4)-(10x^3)+(18x^2)-8 is continuous on the closed interval (1,8). Find the absolute minimum and maximum values for the function on this interval. Please help me!!! And please show your work so that i understand!! Thank you!!

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 function satifies the ...

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]

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
f'(x)=sqrt(x)*sin(x) The first derivative of the f is given above. If f(0)=0, at what value of x does the function f attain its minimum value on the closed interval [0,10]?

Minimum on a Closed Interval
What is the minimum value of the function g(x)= 1/x * sin (pi *x) on the interval [1,2]? I got -2/3. Is this right? thanks.

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 the difference between the Mean Value ...

calc
Consider the function below. (Round the answers to three decimal places. If you need to use - or , enter -INFINITY or INFINITY.) f(x) = 4 + 4x2 - x4 (a) Find the intervals of increase. (Enter the interval that contains smaller numbers first.) Find the intervals of decrease. (...

Calculus
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = 4√x [4, 9]

Calc
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = 4√x [4, 9]

calculus
Find the value or values of c that satisfy the equation f(b)-f(a)/b-a = f'(c) in the conclusion of the mean value theorem for the given function and interval f(x)= x^(2/3) , [0,1]

calculus
If f(x) is differentiable for the closed interval [-3, 2] such that f(-3) = 4 and f(2) = 4, then there exists a value c, -3 < c < 2 such that (4 points) If f(x) = ι(x2 - 8)ι, how many numbers in the interval 0 ≤ x ≤ 2.5 satisfy the conclusion of the...

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 am a bit uncertain on...

Calculus
Let f be a differentiable function defined on the closed interval [a,b] and let c be a point in the open interval (a,b) such that I.f'(c)=0 II.f'(x)>0 when a≤x<c III.f'(x)<0 when c<x<≤b Which of the following statements must be true? (A)f(c)=0 (B)f"(...

Calc
f(x) = x^2 / (x - 7)^2 (a) Find the vertical and horizontal asymptotes. x= y= (b) Find the interval where the function is increasing. Find the intervals where the function is decreasing. (Enter the interval that contains smaller numbers first.) (c) Find the local minimum value...

Calculus
Hello my problem is the next one: g is a function between the interval (a,b)and "p" is a fixed point in (a,b) that`s mean that g(p)=p. If g can be derivated in that interval and /g(x)/<1 to all the interval. Demonstrate using the Mean value theorem that there is ONLY one ...

Calc 1
Consider the following function. f(x) = x^6 ln x (a) Use l'Hospital's Rule to determine the limit as x → 0+. (b) Use calculus to find the minimum value. Find the interval where the function is concave up. (Enter your answer in interval notation.) Find the interval where ...

calculas 1
Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. (Enter your answers as a comma-separated list.) f(x) = x^9, [0, 9]

math calculus
Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (Round your answers to two decimal places. If an answer does not exist, enter DNE.) g(x) = (x^2 − 4)^2/3, [−5, 3] find absolute maximum (x, y) = ...

Calculus
The function f is given by f(x)=3x^2+1. What is the average value of f over the closed interval [1,3]? The answer I get is 12, but the book says it's 14. I don't understand why.

unique solution
How do I show that the equation x^4 + 3x + 1 = 0, -2 <= x <= -1 has exactly one solution in the interval. Thanks. One way to do this is to use trial and error. split the interval (-2,-1) into 10 equal parts. Then evaluate the function at each point. That is put the value...

Math
Find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = 4x3 − 3x2, [−1, 2]

Is this correct?
What values (c) if any are predicted by the mean value theorem for the function f(x)= (x-2)^3 on the interval [0,2]? I got x= 4 and x=0, since x=0 is within the interval I chose that as my answer. Thank you.

math
Find the largest and smallest values of the given function over the prescribed closed, bounded interval. F(x)=e^{x^2-2x} for 0<x<2(It,s bounded interval)

Calculus
I'm supposed to find the average value of the function over the given interval. f(x) = sin(nx), interval from 0 to pi/n, where n is a positive integer. I know the average value formula, and I know that the integral of that function would be (-1/n)cos(nx), but I keep getting ...

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.

calculus
Find a point c satisfying the conclusion of the Mean Value Theorem for the following function and interval. f(x)=x^−1 [1,9]

calculus
Find a point c satisfying the conclusion of the Mean Value Theorem for the function f(x)= x^1/3 on the interval [1,8] I got f'(c)= 1/7 but am not sure where to go from there.

Calculus
Let f be the function defined by f(x)= x^3 + ax^2 +bx + c and having the following properties. 1. the graph of f has a point of inflection at (0,-2). 2. The average value of f(x) on the closed interval (0,-2) is -3. Determine the values of a,b and c

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

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? I plugged 2 and 0 into the original problem and got 3 and -1 . Then I found the derivative to be ((x-1)-(x+1))/(x-1)^2. Whould would I...

math
Consider the function f(x)=10sqrrootx+5 on the interval [3,10]. i found the average slope to be 2.043181217 By the Mean Value Theorem, we know there exists a c in the open interval (3,10) such that f'(c) is equal to this mean slope i tried tking the first derivative of the eq ...

Calculus
On the closed interval, [0, 2*pi], find the absolute maximum of the function f(x)= sin^2(x)

Statistics
1. A certain population follows a normal distribution, with mean m and standard deviation s = 2.5. You collect data and test the hypotheses H0: m = 1, Ha: m 1. You obtain a P-value of 0.022. Which of the following is true? Why? a. A 95% confidence interval for m will include ...

Calc
This problem is really weird. I have to explain why MVT applies for f(x)=2sinx-sin2x 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 that the function is ...

Statistics
Please help!! I have no idea how to do this question. 14. A sample of 40 CD’s from your collection showed a mean length of 52.74 minutes with a standard deviation of 13.21 minutes a. Construct the 95 percent confidence interval for the mean. b. Construct the 95 percent ...

Calculus
Find the absolute maximum & minimum of the function f (x)=e^x for any closed interval [a,b] Justify your answer.

Math
Can someone explain to me.... when you are graphing number sets.... when do you use open/ closed cirles.... When do you use arrows?... What are intergers??? Thanks, ummm kbye<33=]]]] i don't like mathhh its kinda gayy can u stop... you are not helping... BYE! I'm not ...

calculus
The function f is continuous on the closed interval [0,6] and has values that are given in the table below. x |0|2|4|6 f(x)|4|K|8|12 The trapezoidal approximation for(the integral): 6 S f(x) dx 1 found with 3 subintervals of equal length is 52. What is the value of K? How do ...

math (calculus) PLZZZ help!
Consider the function below. (Round the answers to two decimal places. If you need to use - or , enter -INFINITY or INFINITY.) f(x) = e^x/1+e^x find the horizontal and vertical assymptotes? find the interval whr f is increasing? Find the inflection point. Find the interval ...

Mathematics optimization
The arithmetic mean of two numbers a and b is the number(a+b)/2. Find the value of c in the conclusion of the mean-value theorem for f(x)=x^2 on any interval [a,b].

calculus
Let f be the function defined by f(x)= sqrt(x), 0 <or= x <or= 4. and f(x)= 6-x, 4 < x <or= 6 a. Is f continuous at x=4? justify. b. Find the average rate of change of f(x) on the closed interval [0,6]. c. suppose the function g(x)= k sqrt(x), 0 <or= x <or= 4...

geometric mean
The geometric mean of two postitive numbers a and b is sqrt(ab). Show that for f(x) = 1/x on any interval [a,b] of positive numbers, the value of c in the conclusion of the mean value theorem is c = sqrt(ab) I have no idea how to do this! If the mean of a and b is sqrt(ab), ...

calculus
The top and bottom margins of a paster are each 6 cm and the side margins are each 4cm. If the area of printed material on the poster is fixed at 384cm^2, find the dimensinos of the poster with the smallest area. I would like to know if my work is correct. x = width of print y...

math: real numbers
The statement below is false. Correct it by changing two symbols. "The interval (a,b) contains its infimum and its supremum." I'll give you a hint. The interval (a, b) is an open interval. What you need is a closed interval. Parentheses are used for open intervals. What symbol...

calculus II
I have the function f(x)=e^x*sinNx on the interval [0,1] where N is a positive integer. What does it mean describe the graph of the function when N={whatever integer}? And what happens to the graph and to the value of the integral as N approaches infinity? Does the graph ...

Math
18) Find all numbers c that satisfy the conclusion of the Mean Value Theorem for the following function and interval. Enter the values in increasing order. f(x)=2x6x+12,[1,4]

Calculus IVT
The function f is continuous on the closed interval [0,6] and has values that are given in the table above. The equation f(x)=3 must have at least two solutions in the interval [0,6] if k= ? A. 0 B. -1 C. 1 D. 2 E. 3

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 comma-separated list. If it does not...

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 comma-separated list...

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 comma-separated list...

Calculus
Find the largest and smallest values of the given function over the prescribed closed, bounded interval of: f(x)=(3x-1)e^-x for 0<x<2

Calculus
If f(x) is differentiable for the closed interval [−1, 4] such that f(−1) = −3 and f(4) = 12, then there exists a value c, −1< c < 4 such that a)f'(c)=3 b)f'(c)=0 C)f(c)=-15 d)f(c)=3 I understand that you are supposed to use the mean value theorem, but i dont ...

Calculus
In the viewing rectangle [-4, 4] by [-20, 20], graph the function f(x) = x3 - 3x and its secant line through the points (-3, -18) and (3, 18). Find the values of the numbers c that satisfy the conclusion of the Mean Value Theorem for the interval [-3, 3].

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 solving the problem. We...

Calculus
Determine if the Mean Value Theorem for Integrals applies to the function f(x) = 5 - x^2 on the interval 0 to sqrt 5 . If so, find the x-coordinates of the point(s) guaranteed by the theorem.

math calculus
In the viewing rectangle [-4, 4] by [-20, 20], graph the function f(x) = x3 - 3x and its secant line through the points (-3, -18) and (3, 18). Find the values of the numbers c that satisfy the conclusion of the Mean Value Theorem for the interval [-3, 3].

math
does the function f(q)=(q(1-q))^1/2 satisfy the hypothesis of the mean value theorem at the interval [-1,5]

Calculus
Find the average value of the function f(x) 8x^2-9x+8 on the interval [3,5]. Find the value of the x-coordinate at which the function assumes it's average value The average value is ? the x-coordinate is ? Please help and showing work is much appreciated. Thank you

calculus
Use the intermediate value theorm to show that the polynomial function has a zero in the given interval f(x)=x^5-x^4+8x^3-5x^2-14x5;[1.4;1.5] find the value of f(1.4) f(1.4)= find the value of f(1.5) f(1.5)=

Algebra
Use the intermediate theorem to show that the polynomial function value has a zero in the given interval f(x)=x^5-x^4+8x^3-7x^2-17x+7; [1.6,1.8] Find the value of f(1.6) Find the value of f(1.8)

Math
Determine if the Mean Value Theorem for Integrals applies to the function f(x) = x3 - 16x on the interval [-1, 1]. If so, find the x-coordinates of the point(s) guaranteed to exist by the theorem.

Math (Calculus) (mean value theorem emergency)
Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c in the interval (-2,4) such that the tangent ...

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 with commas. c = Do ...

calc
f(x) = e^x/1+e^x find the horizontal and vertical assymptotes? find the interval whr f is increasing? Find the inflection point. Find the interval where the function is concave up. Find the interval where the function is concave down.

Calc 1
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x)=x^3+x-4 [0,2]

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