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

117,096 results

### 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.

### Calculus

The function f is continuous on the closed interval [-5,5], and f(-2) = 6, f(1) = -3, and f(4) = 6. Which of the following statements must be true? A. The equation f(x) = 0 has at least two solutions on the closed interval [-5,5]. B. The equation f(x) = 0 has exactly two ...

### 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 ...

### 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 ...

### Calculus

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

### 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 ...

### 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].

### 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 ...

### 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

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...

### 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 ...