# 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]

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

4. ## slope

Find the slope of the line passing through the given points using the slope formula. Enter the slope in simplest form. Describe the slope as positive, negative, zero, or undefined. (8,2) and (15,9) my answer = 1 the slope is posistive

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.

1. A particle moves along the x-axis in such a way that it's position in time t for t is greater or equal to 0 is given by x= 1/3t^3 - 3t^2 +8t A. Find the position of the particle at time t = 3. B. Show that at time t = 0, the particle is moving to the

7. ## 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

8. ## 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

9. ## 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

10. ## 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

11. ## 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

12. ## 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,

13. ## 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

14. ## 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

15. ## Math (Secant Lines)

Consider the function f(x)=sqrt(x) and the point P(4,2) on the graph of f? -Consider the graph f with secant lines passing through p(4,2) and Q(x,f(x)) for x-values 1, 3, and 5. -Find the slope of each secant line -Use the results to estimate the slope of

16. ## 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

17. ## 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

18. ## trigonometry

An object is attached by a string to the end of a spring. When the weight is released it starts oscillating vertically in a periodic way that can be modeled by a trigonometric function. The object's average height is −20 cm (measured from the top of the

19. ## 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

20. ## 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]

21. ## algebra

please show work Find the average rate of change for the given function on the given interval. 3. f(x)=x2-4x; -2 ≤x≤ 4 4. f(x)=2x-1; [0, 3] Find a Point-Slope equation for a line containing the given point and having the given slope. 9. (-7, 2), m = 3

22. ## 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

23. ## 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,

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 _______

25. ## 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.

26. ## physics

I'm making a graph of force vs stretch for springs. I have 7 data trials with the k (F = kx) ranging from 28 to 31, average is 29.6. Now I need to find the slope and write an equation for the graph. If I use the first two points to get the slope, I get a

27. ## 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

28. ## 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'(

29. ## 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

30. ## Math

Without graphing (PLEASE DO IT IF NEEDED THIS IS JUST A PRACTICE PROBLEM) tell whether the slope of a line that model s the linear relationship is positive, negative, zero, or undefined. Then find the slope. A babysitter earns $8 for 1h and$40 for 5h. A.

31. ## Calculus

Mathematica Project - Position, Velocity, and Acceleration? A rocket is fired vertically upward into the air from a launching platform 100 ft above the ground. The platform is then retracted, and the rocket is allowed to fall to the ground. The height (in

32. ## 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

33. ## 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

34. ## 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),

35. ## Calculus

for function f(x)=4x-2x^3 a.) Find the general formula for the slope of the tangent line using the definition of derivative. b.) Find the slope at x=1

36. ## 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

37. ## 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

38. ## 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

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.

40. ## 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

41. ## 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.

42. ## 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

43. ## 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

44. ## 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

45. ## 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

46. ## 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?

47. ## 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

48. ## 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

49. ## 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

50. ## 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

51. ## 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.

52. ## 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)

53. ## 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

54. ## 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"

55. ## 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

56. ## 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

57. ## 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¯¯¯.

58. ## 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),

59. ## 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

60. ## 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

61. ## 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

62. ## 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

63. ## 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),

64. ## Physics

can someone help i'm stuck on two questions??? 23. On a velocity-time graph, when is the object not moving? when the slope is a straight line rising to the right when the slope is a straight line falling to the right when the slope is a line curving upward

65. ## 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

79. ## 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

80. ## Algebra 1

algebra questions I don’t need any of the open a textbook answers. I have worked hard to get my algebra done but these last units have turned my mind into mush. I don’t just want answers I need an explanation. Any help would be wonderful Thank you 2)

81. ## MATH

HHHHHEEEEEELLLLLLLPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Find the y intercepts of these please: 1. The slope is: 6/2...3/1...3 2. The slope is: 10/2... 3. The slope is: 2/2...2 4. The slope is: 2/2...2 The formula for a slope intercept is: y = mx +

82. ## 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

83. ## 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

84. ## 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

85. ## calculus

For the function y = 9x2 + 6x + 2, at the point x = 7, find the following. (a) the slope of the tangent to the curve (b) the instantaneous rate of change of the function

86. ## math

a) A linear function f(t)=b + mt has a slope of -4 and vertical intercept of 20. Find its equation. b) An exponential function g(t)=Ca^t has a decay factor of 1/4 and an initial value of 20. Find its equation. Plot both functions

87. ## 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

88. ## 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

89. ## 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)

90. ## 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

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

92. ## Math

f(x)=2x^(3)–1x^(2)+3x–2 Find the average slope of this function on the interval (1,7).

93. ## math, slope

how to find average slope: you are given points of: (0,0) (20,.166) (40,.181) (60,.194) (80,.204) (100,.210) (120,.214) how do i find average slope of all of these?

94. ## Helpppp Math!!!

The market value (in thousands of dollars)of a certain home is a linear function of t, the time in years since 1990. In 1992 the market value was 68 thousand dollars, while in 1997 the market value was 79 thousand dollars -Find the slope of V as a linear

95. ## 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.

96. ## math

Let the total cost function C(x) be defined as follows. C(x) = 0.0008x3 - 0.04x2 + 99x + 4400 Find the average cost function C. C(x) = ?? Find the marginal average cost function C '. C '(x) = ??

97. ## Calculus

How do you find Altitude and slope slope is the derivative of a function: for ex. if you have f(x)=x^2 + x, at point (1,2) f'(x)=2x+1 your slope is 2(1) + 1 = 3 =m to find the equation is y-y1=m(x-x1) so you have: y-2=3(x-1) gives you: 3x-1 is your

98. ## math

Consider the function:(-2x^2 +3x -7) y= -2x^2x +3x +17 Find y ′ using implicit differentiation. Do not solve for y. What is the slope of the tangent at (x,y) = (−1,−1)? Find y ′ by solving for y and using the quotient rule. What is the slope of the

99. ## math

Consider the function: (-2x^2 - 2x-4) y = 2x^2 - x +10 Find y â€² using implicit differentiation. Do not solve for y. What is the slope of the tangent at (x,y) = (2,âˆ’1)? Find y â€² by solving for y and using the quotient rule. What is the

100. ## 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