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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geometry

what is the diffwereence between a postulate and theorom

Algebra

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...

algebra 2

list all the possible rational roots of P(x) given by the Rational Root Theorom. P(x)=4x^4-2x^3+x^2-12

chemistry

[(exp value - accepted value)/accepted value]*100 = percent error. For exp value, do I have to average my five trials?

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

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 as a conservative value (upper bound) for the ...

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 ...

maths

prove that 1+x < e^x < 1+ xe^x for x>0 using the mean value theorem

Math

If f(x)= 3/x-4 and g(x)=2x, there is at least one value of x for which the composite function f(g(x)) cannot be evaluated. What is that value of x? For what value(s) of x is it impossible to evaluate g(f(x))? How do you figure this out?

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?

What is the formula for percent-error? It's either: %error= (your value/accepted value)*100 or %error= (accepted value/your value)*100 I'm pretty sure it's the first one, but I also heard it can go either way. I tried both ways but I end up with two different values. Which one...

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 ...

Quantitative Methods

Assume you have applied to two different universities (lets refer to them as Universities A and B) for your graduate program. In the past 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the ...

Quantitative Methods

Assume you have applied to two different universities (lets refer to them as Universities A and B) for your graduate program. In the past 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the ...

Computer science

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

physics

. Consider a large number, N(0) , molecules contained in a volume V (0) . Assume that there is no correlation between the locations of the molecules (ideal gas). Do not use the partition function in this problem. (a) Calculate the probability P (V; N) that an arbitrary region ...

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 ...

Chem

what is the meaning of "accepted value" with respect to an experimental measurement? Accepted value means that the majority of reasonable folks will accept that value as true. O thanks.. one more question When brought to the surface of the moon, will a mass have more or less ...

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

An automobile travels 4 miles road in 5 minutes. Use the Mean Value theorem to show that the speedometer reads exactly 48 mph at least once during the trip.

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

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...

chemistry

2. If the accepted enthalpy change value for the dissolving of sodium hydroxide in water is −44.2 kilojoules per mole, determine the percent error of the experimental value that you calculated in Part I. Show your work. (experimental - actual value) / actual value × 100 %

Polynomials help

Hello, this is a question which i don't know how to do. Find the value of k for which a-3b is a factor of a^4-7a^2b^2 + kb^4 Hence, for this value of k, factorise a^4 - 7a^2b^2 + kb^4 completely. I tried to do long division for the question, but couldnt. Is there any other ...

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 ...

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

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 ...

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 + 6x-1 , [-3, -2] Round your answer to two decimal places.

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

Use the graph of f(x)=x^2/(x^2-4) 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 is continuous and ...

Algebra 1

Which statement is always a correct conclusion about the values x and y in the function y=x-3? a. The value of x is always 3 less than the value of y b. The value of y is always less than the value of x c. When the value of x is positive, the value of y is also positive d. As ...

calculus

Consider the function f(x) = x^3-3x^2+2x-18 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 exists a c such that f...

Stats

2 samples were collected to determine whether there was a difference between two weight loss methods targeting men. The average weight loss method is provided for the 2 samples along with the respective standard deviations. Is the second method - with an average weight loss of...

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.

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.

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

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, ...

Math- Trig

1. Determine the exact value of cos^-1 (pi/2). Give number and explanaton. 2. Determine the exact value of tan^-1(sq. root 3). with explanation. 3. Determine exact value of cos(cos^-1(19 pi)). with explanation. 4. Determine the exact value of sin(sin^-1(20 pi)). with ...

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...

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

Consider the function f(x) = 2 x^3 - 12 x^2 - 30 x+ 10 on the interval [ -6 , 8 ]. Find the average or mean slope of the function on this interval. Average slope = By the Mean Value Theorem, we know there exists at least one c in the open interval ( -6 , 8 ) such that f'( c) ...

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

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]

physics

2. What value did you calculate for the index of refraction of the glass block in Part 2? How does your value compare to the accepted value of 1.53? Calculate the percentage error. Different materials have distinct indexes of refraction. Explain how you might identify a ...

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) 5-12x+3x^2 [1,3]

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

Let f be a twice-differentiable function such that f(2)=5 and f(5)=2. Let g be the function given by g(x)= f(f(x)). (a) Explain why there must be a value c for 2 < c < 5 such that f'(c) = -1. (b) Show that g' (2) = g' (5). Use this result to explain why there must be a ...

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...

algebra

why is the graph of an inverse flipped over the line y=x instead of another line? The inverse function of f(x) tells you what value of x you get for a given value of y. When you flip the graph about the 45 degree y=x line, it is the same as using the value of y on the original...

Math - Mean Value Theorem

Suppose f(x)=αx^2+βx+γ is a general quadratic polynomial with α≠0 and let [a,b] be any interval. According to the Mean Value Theorem there is at least one number c such that f(b)−f(a)=f′(c)(b−a). In this particular case the number c is unique and it's independent ...

Math

is x=5 a function No. The plot (graph) is a vertical line at x=5, so y can have many different values, in fact, any value. a function has one y value for each x value. thanks

College alegbra

A rancher wants to create a fence enclosing 1500 m2 of land. The plot will be divided into two equal areas by an additional fence parallel to two sides as shown in the diagram below. Find the dimensions of the plot which results in using the least amount of fencing. a. Write ...

Qvntitative Methods

CASE STUDY: 1 The bulbs manufactured by a company gave a mean life of 3000 hours with standard deviation of 400 hours. If a bulb is selected at random, what is the probability it will have a mean life less than 2000 hours? Question: 1) Calculate the probability. 2) In what ...

science

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...

Maths

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 ...

math

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...

Math Help!

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+...

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...

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...

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