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)

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  1. 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]

  2. Math please help.

    Find the function that has the greater rate of change As x increases by 1, y increases by 3. The graph- x: -1 | 0 | 1 y: 0 | 2 | 4 A. the slopes are equal B. the graph has a greater slope C. the function rule has a greater slope**** D. none of the above

  3. Algebra 1

    Question 9 Examine the graph of f(x) f ( x ) and the table that contains values of g(x). g ( x ) . Curve f of x approaches Y equals negative 7 on the left and positive infinity on the right. It passes through points (0, negative 4) and (1, 2). © 2018

  5. slope

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  6. Math please check my answers?

    1) The linear function f(x) contains the points (-10, -29) and (-2, 83). If g(x) = 25x - 50, which statement is true? A. The functions f(x) and g(x) both have positive slopes.

  7. Calculus Please Help

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  8. 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

  10. calculus

    1. Find the average value have of the function h on the given interval. h(x) = 2 cos4(x) sin(x), [0, π] 2. Consider the given function and the given interval. f(x) = 6 sin(x) − 3 sin(2x), [0, π] (a) Find the average value fave of f on the given

  11. Algebra

    The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −5 0 −1 1 3 g(x) g(x) = 2x − 7 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the

  12. Algebra 1

    The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −5 0 −1 1 3 g(x) g(x) = 2x − 7 Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the

  13. Math

    Examine the graph of f(x) and the table that contains values of g(x). Curve f of x approaches Y equals negative 7 on the left and positive infinity on the right. It passes through points (0, negative 4) and (1, 2). x g(x) −1 1 0 3 1 9 2 27 3 81 Which

  15. College algebra!

    For the linear function f(x) = 5x + 3 (a) Determine the slope and y-intercept (b) Use the slope and y-intercept to graph the linear function. (c) Determine the average rate of change of the function (d) Determine whether the linear function is increasing,

  16. Calculus

    The cost to produce x items is given by the function C(x) = 1200 + 8x + 0.01x^2. a) Write a function that represents the average cost of producing x items. b) Use the derivative of the function from a) to find the number of items that should be produced to

  17. 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

  18. Math (Secant Lines)

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  20. Math

    1. Function Q and function R are both linear functions. Function Q has an x-intercept at (4,0), and the slope is 1/4. Function R is represented by the table. x y -4 14 3 0 5 -4 Which statement is true? A. Function Q has a larger y-intercept and a less

  21. Calculus

    For the function ƒ(x) = x2 find the slope of secants from the point (2, 4) to each of the following points. (3, __ ) (2.5 , __ ) (2.1 , __ ) (2.01, __ ) (2.001, __ ) Using the pattern from question 1, what do you think the slope of a tangent at the point

  22. trigonometry

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  23. 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

  25. Calculus

    If f is a function such that [(f(b)-f(a))/(b-a)]=2 , then which of the following statements must be true? a.f(a) = f(b) = 2 b.The slope of the tangent line to the function at x = a is 2. c.The average rate of change of the function on the interval [a, b]

  26. algebra

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  27. calculus totally confused

    find a first degree polynomial function p(1) whose value and slope agree with the value and slope of f at x=c. i think you use taylor series for this f(x)=4/sqrt(x), c=1 i'm totally confused on how to do it. i know you find the derivative but how do i get

  28. algebra

    Unit Exam 3 9 of 169 of 16 Questions Question Examine the graph of f(x) and the table that contains values of g(x). Curve f of x approaches Y equals negative 7 on the left and positive infinity on the right. It passes through points (0, negative 4) and (1,

  30. 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 _______

  31. math

    Which statement correctly describes the slope of the linear function that is represented by the data in the table? x y 8 –8 8 –4 8 0 8 4 8 8 The slope is positive. The slope is negative. The slope is zero. There is no slope.

  32. physics

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  33. algebra

    In 2000, 49% of the residents in a large city regularly used newspapers for getting news and this has decreased at an average rate of approximately 1.3% per year since then. Find a linear function in slope-intercept form that models this description. The

  35. calculus

    Consider the function f(x) = 1/x on the interval [ 4 , 11 ]. (A) Find the average or mean slope of the function on this interval. Average Slope =_______ (B) By the Mean Value Theorem, we know there exists a c in the open interval ( 4 , 11 ) such that f'(

  36. 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

  37. Math

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  40. calculus

    Consider the function f (x)=7−6x^2 on the interval [ − 3 , 3 ] . Find the average or mean slope of the function on this interval, i.e. f(3)-f(-3) / 3-(-3)= By the Mean Value Theorem, we know there exists a c in the open interval (−3,3) such that

  41. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4. Find all values of x on the

  42. Algebra

    1. Determine whether the relation is a function. {(-2, -7), (3, -5), (6, -4), (9, -6), (10, -1)} 2. Determine whether the relation is a function. {(-5, -4), (-2, 9), (-1, -2), (-1, 7)} 3. Determine whether the relation is a function. {(-7, -1), (-7, 2),

  43. Calculus

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  45. Algebra

    HOURS STUDYING AVG GRADE 0 62 1 78 2 85 5 74 WHICH TYPE OF FUNCTION IS MOST LIKELY TO MODEL THESE DATA? A. LINEAR FUNCTION W/POSITIVE SLOPE B. LINEAR FUNCTION W/NEGATIVE SLOPE C. NON-LINEAR THAT DECREASE THE INCREASE D. NON LINEAR FUNCTION THAT INCREASES

  46. Algebra

    HOURS STUDYING----- AVG GRADE 0-------------------- 62 1-------------------- 78 2-------------------- 85 5-------------------- 74 WHICH TYPE OF FUNCTION IS MOST LIKELY TO MODEL THESE DATA? A. LINEAR FUNCTION W/POSITIVE SLOPE B. LINEAR FUNCTION W/NEGATIVE

  47. pre-cal: graphs of functions- fill in the blank

    To find the domain of a function from its graph... To find the range of a function from its graph... To approximate the relative minimum or maximum of a function using a graphing utility,... Let a(,f(a)) and (b,f(b)) be two points on the graph of a

  48. Algebra please check my answers

    1) The linear function f(x) contains the points (-10, -29) and (-2, 83). If g(x) = 25x - 50, which statement is true? A. The functions f(x) and g(x) both have positive slopes.

  50. calculus

    Consider the function f(x) = 1/x on the interval [ 4 , 11 ]. (A) Find the average or mean slope of the function on this interval. Average Slope = (B) By the Mean Value Theorem, we know there exists a c in the open interval ( 4 , 11 ) such that f'( c) is

  51. Algebra 116

    I have like 13 questions i need help with so here they go. 1. In 1991 the life expectancy of males in a certain country was 70.1 years. In 1995 it was 72.6 years. Let E representn the life expectancy in years and t represent the number of years since 1991.

  52. calculus

    8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9. Find f '(x) for f(x) = xln(x) - 5ex. 10. Find f '(x) for f (x) = e(^lnx) + e^(x)ln(x) 11. Find the x-coordinate where the graph of the function f(x) = e^(-cosx) has a slope of 0. 12. If

  53. math

    Consider the function f ( x ) = 3 − 5 x^2 on the interval [ − 2 , 8 ] . Find the average or mean slope of the function on this interval, i.e. f(8)-f(-2)/8-(-2)= By the Mean Value Theorem, we know there exists a c in the open interval ( − 2 , 8 ) such

  55. calc

    (1 point) Consider the function 𝑓(𝑥)=7−6𝑥2 on the interval [−6,3] (A) Find the average or mean slope of the function on this interval, i.e. 𝑓(3)−𝑓(−6)/(3−(−6))= (B) By the Mean Value Theorem, we know there exists a 𝑐 in the

  56. 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

  57. ECONOMICS

    solution:the total cost function of a firm is given by C=.04q^3-.9 q^2+10q+10.find slope of average cos?

  58. calculus

    Some scientists believe that the average surface temperature of the world has been rising steadily. They have modeled the temperature by the linear function T = 0.02t + 8.75, where T is temperature in °C and t represents years since 1900. (a) What do the

  60. Maths

    Demand function P=50-Q Average Cost 5Q + 40 +10/Q Calculate the firm's total cost function Find the marginal cost function and evaluate it at Q=2 and Q=3 What is the total revenue function Find the firms's revenue maximising output level Find the firm's

  61. 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

  62. math

    Find the average cost function C associated with the following total cost function C. C(x) = 0.000007x3 - 0.06x2 + 110x + 76000 C(x) = ?? (a) What is the marginal average cost function C' ? C'(x) = ?? (b) Compute the following values. (Round your answers

  63. Calculus

    Find the average value of the function over [1,3] and all values of x in the interval for which the function: f(x)= 4(x^2+1)/x^2 equals its average value.

  65. Calculas

    The slope of the tangent line to the graph of a function, h(t) is 7/2t The function passes through the point (5,3) Find h(4)

  66. mathematics

    Q1: A linear function is given. g(x) = −5x + 9 (a) Find the average rate of change of the function between x = a and x = a + h. ---------------------------------------------------------------------------------------------------- Q2: A function f is

  67. 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"

  68. Calculus

    If f is a function such that (f(b) - f(a))/(b-a) =2, then which of the following statements must be true a) f(a) = f(b) =2 b) the slope of the tangent line to the function at x =a is 2 c) The average rate of change of the function on the interval [a,b] is

  70. calculus

    find the point on the graph of the given function at which the slope of the tangent line is the given slope x^3+9x^2+33x+15 slope= 6

  71. 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¯¯¯.

  72. Math

    An instructor gives regular 20-point quizzes and 100-point exams in a mathematics course. Average scores for six students, given as ordered pairs (x,y) where x is the average quiz score and y is the average test score, are (18, 87), (10, 55), (19, 96),

  73. AP calculus

    Find the equation of the normal to the curve f(x) = 3cos(2x) at the point x = 0. In class, we learnt to find the derivate of the function, which would represent the slope. After I did that, I found the slope to be 0.. but that is not what my graphing

  75. calculus

    At the indicated point for the function, find the following. A graphing utility's numerical derivative feature can be used to check your work. y = (x3 + 2x)3 at x = 3 (a) Find the slope of the tangent line. (b) Find the instantaneous rate of change of the

  76. Help please I am lost, algebra

    I have notes on this from online but they are different from this problem and I don't know how to solve it. Find the equation of a line with the given information: slope -5/4 and g(14)=-6 It is asking for, point slope form, slope intercept form, Function

  77. algebra

    Will someone please look over these? I am so lost on these. 1. find the domain of p(x)=xsquared+10- I said {x|x is a real number 2. find the intercepts of 3x+2y=6- I got (0,3) and (2,0) 4.find the equation of (-6,-6)and (6,6)- got y=x 7. slope and

  78. 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),

  80. Physics

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  81. Math

    Find 2 tangent line equations to the curve y=x^3+x at the points where the slope of the curve is 4. What is the smallest possible slope of the curve? At what x-value(s)does the curve have this slope? So far I have figured out the derivative of this

  82. algebra

    In most businesses, increasing prices of products can negatively impact the number of customers. A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their

  83. math

    **Problem 3: Create a linear function (y=mx+b) and graph the line for the following set of data. x | y 2 | 1 4 | 2 6 | 3 First, use the slope formula to find slope: (y2-y1)/(x2-x1) Then, put the slope (m), a 'y' point, and matching 'x' point into the

  85. Math

    1. The table shows the number of soccer clubs and the population densities of different cities in a state. City Pop. per square mile Clubs 1 160 6 2 173 8 3 254 7 4 284 11 5 315 9 6 322 10 7 459 14 8 487 20 Based on this information, which statement is

  86. 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

  87. 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

  88. calculus

    Consider the function f(x) = 3 -2 x^2 on the interval [ -5 , 3 ]. (A) Find the average or mean slope of the function on this interval, i.e. \displaystyle{\frac { f(3) - f(-5) }{ 3 - (-5) } = } 4 (B) By the Mean Value Theorem, we know there exists a c in

  90. 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

  91. 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

  92. 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

  93. math

    what is the average or mean slope of the function f(x)=(10(x^1/2)+4 on the interval [2,6]

  95. Math

    1. The slope of the tangent line to a function at a point is equivalent to __. a. the slope of the secant at that point b. the slope of the cosecant at that point c. the rate of change of the function at that point d. the slope of the secant near that

  96. math

    1. Suppose you are at the gas station filling your tank with gas. The function C(g) represents the cost C of filling up the gas tank with g gallons. Given the equation: a) What does the number 3.03 represent? The amount of gas gallons that you pumped b)

  97. geometry

    1. In 1994, the average monthly energy bill for your neighbors family of four was $175. In 2005 their average monthly bill rose to $250. A. Let x=number of years since 1994 and let y= average monthly bill. Write to ordered pairs that follow the info given

  98. Calc

    Recent studies indicate that the average surface temp. of the earth has been rising steadily. Some scientists have modeled the temp. by the linear function T= 0.02t + 8.50, where T is temp. in degrees Celsius and t represents years since 1900. What do the

  100. Algebra 1

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  101. MATH

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  102. Math/Chemistry

    We were given an assignment to find a formula for finding the density of water. I wasn't in class when the assignment was given, but the teacher gave the class two values: density H2O at 20 degrees C= .998823 g/mL density H2O at 25 degrees C= .99707 g/mL A

  103. algebra

    is this right? I need to write a linear function that fits this data and round to the nearest tenth. In 1991 the life expectancy in males was 68.8 and in 1995 it was 71.9.... and so on. I first got the slope m= 71.9-68.8 / 4-1 m = 3.1/3 I fit the slope

  105. Math Calculus

    Economists use production functions to describe how output of a system varies with another variable such as labour or capital. For example, the production function P(L) = 200L + 10L^2 - L^3 goves the output of a system as a function of the number of

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  107. math

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    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

  110. 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

  111. calculus

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    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

  113. Calculus Please help!

    f(x) -2x^3+2x^2-3x+2 Find the average slope of this function on the interval (–3–1) ________

  115. Math

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  116. math, slope

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  117. Helpppp Math!!!

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  118. Calculus

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  120. math

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  121. Calculus

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  122. math

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  123. math

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  125. Math (UBC)

    Economists use production functions to describe how output of a system varies with another variable such as labour or capital. For example, the production function P(L) = 200L + 10L^2 - L^3 goves the output of a system as a function of the number of

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