# a) prove that the function x^3 + 9x^2 +33x assumes the value -8 at least once b)using the mean value theorom or rolle's theorom - no other methods will be accepted - prove carefully that x^3 + 9x^2 + 33x

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### Calculus

a) prove that the function x^3 + 9x^2 +33x assumes the value -8 at least once b)using the mean value theorom or rolle's theorom - no other methods will be accepted - prove carefully that x^3 + 9x^2 + 33x takes on the value -8 at most once

### physics

Compare the slope of the velocity-time graph to the average of all your acceleration values. Are they close? What does the slope of a velocity (or speed) vs. time graph mean? Explain the answer using your data. How does the value of g that you calculated compare to the ...

### Math - Calculus

Show that the equation x^3-15x+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 TI-84, I have no idea how to accomplish this.

### Math - Calculus

Show that the equation x^3-15x+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 TI-84, I have no idea how to accomplish this.

### MATH

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I'm trying to solve this Pythagorean Theorom problem. x^2+(2x^2)=32^2 which becomes 5x^2=1024 I don't get how the x^2 and the 2x^2 combine to get 5x^2. I think it should be 3x^2. Can you explain? Thanks!

### Physics

How do i do this ? ? ? : Suppose you have collected the data shown below for the circuit in Figure 1. Voltage is measured across the resistor. Current is measured through the resistor. The exact value of the resistor is 100 Ω. Figure 1. DESCRIBE THE MEASURED QUANTITIES...

### 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...

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### 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

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 ...

### Math (functions)

For tax purposes, you may have to report the value of your assets, such as cars or refrigerators. The value you report drops with time. "Straight-line depreciation" assumes that the value is a linear function of time. If a $1020 refrigerator depreciates completely in seven ...

### ALGEBRA

wo quadratic functions are shown. Function 1: f(x) = 4x2 + 8x + 1 Function 2: x -2 -1 0 1 g(x) 2 0 2 8 Which function has the least minimum value and what are its coordinates? Function 1 has the least minimum value and its coordinates are (−1, −3). Function 1 has ...

### Calculus

For f(x)=x^2/3(x^2-4) on [-2,2] the "c" value that satisfies the Rolle's Theorem is A. 0 B. 2 C. +or-2 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)

### Calculus

Suppose that you can calculate the derivative of a function using the formula f(x) = 2f(x) + 4x. If the output value of the function at x=4 is 3 estimate the value of the function at 4.012. Linear Approximation right? I'm not seeing an f'(x) anywhere. Can you retype your ...

### math

For tax purposes, you may have to report the value of your assets, such as cars or refrigerators. The value you report drops with time. "Straight-line depreciation" assumes that the value is a linear function of time. If a $1020 refrigerator depreciates completely in seven ...

### Math

I want to know that if we have a set of data and we have to conclude if it is Da Vinci Theorom how do we know if it is or not . what do we need to de in order to conclude thankyou

### 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 increasing on ...

### 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 ...

### Probability

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### Probability

Let X be a continuous random variable. We know that it takes values between 0 and 3, but we do not know its distribution or its mean and variance. We are interested in estimating the mean of X, which we denote by h. We will use 1.5 as a conservative value (upper bound) for the...

### ap calc

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

### Stats

National Packing Materials Company claims its X20 box can hold loads up to at least 80 pounds. Smith Widget Company has been using the boxes for one year and feels the boxes fail at lighter loads. Hearing the complaints from Smith, the lead engineer for National Packaging ...

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### Math

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### 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

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...

### calculus

Find the average value of the function f(x)=8x^2-5x+6 , on the interval [3,5]. Find the value of x-coordinate at which the function assumes it's average value. what is the average value = to ? what is the x coordinate = to ? Thanks

### 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 roots, but f'(x) is ...

### Probability

Let X be a continuous random variable. We know that it takes values between 0 and 3, but we do not know its distribution or its mean and variance. We are interested in estimating the mean of X, which we denote by h. We will use 1.5 as a conservative value (upper bound) for the...

### chemistry

In a laboratory experiment, the density of a concentrated sugar solution was determined by measuring the volume of the solution and corresponding mass. Three students each made a set of measurements using a different balance and used the results to calculate density. Their ...

### Math(ANSWERCHECK)!!

percent error formula= |experimental value -accepted value| / |accepted value| * 100% % error = |0.846 g/mL - 0.78948 g/mL| / |0.78948 g/mL| *100% = 7.31 % Is 7.31% correct or was there a calculation mistake?

### 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 ...

### CALCULUS!

suppose that 3 <_ f prime of x <_ 5, for all values x. show that 18<_ f(8)-f(2) <_ 30 <_ signs mean less or equal to... im supposed to apply mean value theorem or rolle's theorem... i don't understand neither so i cant do the question! please help!

### 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]. ...

### calculus 2

Suppose that you can calculate the derivative of a function using the formula f'(x) = 4f(x) + 2x. If the output value of the function at x= 4 is 2 estimate the value of the function at 4.013

### Percent error?

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### Chemistry

Confused, conflicting texts when you are finding % error for density formula: experienced value-accepted value/ accepted value ×100. Does the ×100 cancel out the percent sign? EX; 7.28g/mL-6.54g/mL/6.54g/mL ×100. Is the answer 11.31 or 11.31% The lab video did not multiply ...

### 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.

### 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 ...

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### Quantitative Methods

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If the last value of Period is less than the number of periods specified in the Parameters worksheet, increment the Period value by 1, otherwise blank the cell(i.e. ""). What does this mean in spreadsheer syntax for excel using the IF function

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### 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).

### Chem (Check)

The accepted value of a length measurement is 200cm, and the experimental value is 198cm. Circle the letter of the value that shows the precent error of this measuerment. a)2% b)-2% c)1% d)-1% is it b)-2% No. What is 2/200 * 100? Percent error = deviation/GAAT * 100 gAAT ...

### 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!

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 ...

### 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 on [a.b] and it is ...

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### 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.

### 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 ...

### calculus

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### Calculus

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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

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...

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### 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 here) at ...

### URGENT!! PLEASE Calc

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### statistics

Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value less than 45.

### statistics

Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value less than 44.

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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.

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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

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, ...

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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).

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### 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 ...

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### 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 I got D. I plugged in...

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### Math - Mean Value Theorem

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A protein polypeptide chain exists in α-helical conformation in a solvent and it has a value of -30,000 deg cm2 dmol-1 for the mean residue ellipiticity at 222 nm ([θ]222) in the temperature range 20-50°C. On raising the temperature above 50°C,[θ]222 increases...

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A perfectly cylindrical container standing upright with a top and bottom(an oil drum or coke can for example) of area A has an empty mass of M and a height of H. It is filled with a liquid of uniform density(p)up to the height of h. When the container is full the centre of ...

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14.what value of n will result in a mean if 31 15.what value of n will result in a median of 23 15.what value of a will result in a range of 84 14,46,19,10,39,22,24,77,n Refresh your memory about the defnition of median, mode and range of a set of numbers. Then pick a value of...

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A.) Determine "a" and "k" so both points are on the graph of the function. 1.) (0,1) (2,1); y=a(x-1)^2+k 2.) (1,11) (2,-19); y=a(x+1)^2+k B.) Determine whether or not the function f(x)=0.25(2x-15)^2+15 has a mazimum or a minimum value. Then find the value. C.) When y=2(x-3)(x+...

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Let X be a continuous random variable. We know that it takes values between 0 and 3, but we do not know its distribution or its mean and variance. We are interested in estimating the mean of X, which we denote by h. We will use 1.5 as a conservative value (upper bound) for the...