# the graph of a sin function has a maximum value of 6 and minimum values of 2 find amplitude Determine the amplitude of the function Determine the vertical translation of the function

50,611 results
1. ## calculus

2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,2pie] . a. Find the absolute maximum and minimum values of f(x) b. Find the intervals on which f is increasing. c. Find the x-coordinate of each point of inflection of the graph of f.

2. ## Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2 a.) Find the values of a and b #2. Let h be a

3. ## AP CALC. AB

Let h be a function defined for all x≠0 such that h(4)=-3 and the derivative h is given by h'(x)=(x^2-2)/(x) for all x≠0 a). Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a local maximum, a local

4. ## Calculus

Find the values of x that give relative extrema for the function f(x)=3x^5-5x^3 A. Relative maximum: x= 1; Relative minimum: x=sqrt(5/3) B. Relative maximum: x=-1; Relative minimum: x=1 C. Relative maxima: x=+or- 1; Relative minimum: x=0 D. Relative

5. ## Calculus

Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. a.Find all values of x where the graph of g has a critical value. b.For each critical value, state whether the

6. ## Calculus

Consider the function f(x)=sin(5x)/x. (a) Fill in the following table of values for f(x): x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1 f(x)= ( I need the values of f(x) for each x) (b) Based on your table of values, what would you expect the limit of

7. ## Algebra 2

1. By graphing the system of constraints, find the values of x and y that maximize the objective function. 2

8. ## math

What are the coordinates of the vertex of the graph? Is it a maximum or a minimum? a. (−2, −1); maximum b. (−1, −2); maximum c. (−2, −1); minimum d. (−1, −2); minimum the graph shows the shape like a U and it's towards the negative area

9. ## math

Given the minimum and maximum values of the function y=3sin(x). My anser is -3 for min and 3 foe max by looking at the graph on my calculator. I want to know how solve for it on paper without looking at the graph.

10. ## Mathematics

A sine function has the following key features: Period = 4 Amplitude = 3 Midline: y=−1 y-intercept: (0, -1) The function is not a reflection of its parent function over the x-axis. Use the sine tool to graph the function. The first point must be on the

11. ## algebra

A sine function has the following key features: Period = 4 Amplitude = 4 Midline: y = 1 y-intercept: (0, 1) The function is not a reflection of its parent function over the x-axis. Use the sine tool to graph the function. The first point must be on the

12. ## math

the graph of a sin function has a maximum value of 6 and minimum values of 2 find amplitude Determine the amplitude of the function Determine the vertical translation of the function

A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For each of the following

14. ## Calculus

Please check my answers! My teacher never gave us the answer sheet so I have no idea what to study TT (also please give the correct answers to the ones I got wrong ^0^) 1. lim as x-> inf. of (9x-x^2-7x^4)/(x^3+12x) 9 -7/12 -7 DNE

15. ## Mathematics

A sine function has the following key features: Frequency = 1/4π Amplitude = 2 Midline: y = 2 y-intercept: (0, 2) The function is not a reflection of its parent function over the x-axis. Use the sine tool to graph the function. The first point must be on

A continuous function f, defined for all x, has the following properties: 1. f is increasing 2. f is concave down 3. f(13)=3 4. f'(13)=1/4 Sketch a possible graph for f, and use it to answer the following questions about f. A. For each of the following

17. ## Math

The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D)

18. ## Math

Can someone help me with these questions? 1.What are the maximum and minimum values for Y=28(1.21)^x on the interval 0

19. ## graphing help?

Graph ​ g(t)=4sin(3t)+2 ​. Use 3.14 for π . Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point. How would I graph this? I have

20. ## Algebra

A sine function has the following key features: Period = 4 Amplitude = 4 Midline: y = 1 y-intercept: (0, 1) The function is not a reflection of its parent function over the x-axis. Use the Desmos graph tool to graph the function. The first point must be on

21. ## Mathematics

A sine function has the following key features: Period = π Amplitude = 2 Midline: y= −2 y-intercept: (0, -2) The function is a reflection of its parent function over the x-axis. Use the sine tool to graph the function. The first point must be on the

22. ## calculus

Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2), with x ≠ 2. Find all values of x where the graph of g has a critical value. For each critical value, state whether the graph

23. ## Please check my Calculus

1. Find all points of inflection: f(x)=1/12x^4-2x^2+15 A. (2, 0) B. (2, 0), (-2, 0) C. (0, 15) D. (2, 25/3), (-2, 25/3) E. none of these I got D. I found the second derivative and equaled it to 0 and solved for x. I plugged the x values in to get my

24. ## Mathematics

Use a graphing utility to graph the function and to approximate any relative minimum or relative maximum values of the function. (Round your answers to two decimal places. If an answer does not exist, enter DNE.) f(x) = 3x2 − 2x − 5

25. ## Calc

Various values for the derivative, f'(x), of a differentiable function f are shown below. x=1, f'(x) = 8 x=2, f'(x) = 4 x=3, f'(x) = 0 x=4, f'(x) = -4 x=5, f'(x) = -8 x=6, f'(x) = -12 If f'(x) always decreases, then which of the following statements must

26. ## calculus

2. Consider the function f defined by f(x)=(e^X)cosx with domain[0,2pie] . a. Find the absolute maximum and minimum values of f(x) b. Find the intervals on which f is increasing. c. Find the x-coordinate of each point of inflection of the graph of f.

27. ## Algebra2

Complete parts a – c for each quadratic function. a. Find the y-intercept, the equation of the axis of symmetry and the x-coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. 1. f(x)

28. ## calculus

f(x)=x^4-4x^3-x^2+12x-2. Identify the local maximum by circling the point on the graph, b. Identify the local minimum by putting a small square around the point on the graph. c. Use your calculator's minimum function to find the coordinates of the absolute

29. ## math

Answer the following questions for the function f(x)=sin^2(x/5) defined on the interval .(-15.507923,3.82699075) Rememer that you can enter "pi" for as part of your answer. a.what is f(x) concave down on the region B. A global minimum for this function

30. ## Pre-Calculus

Use a graphing utility to graph the function y = d + a sin (bx - c) for different values of a, b, c, and d. Write a paragraph describing the changes in the graph corresponding to changes in each constant.

31. ## algebra

Find the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=-2x^2+2x+9

Can someone check my answers: 1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { |x|, -2

33. ## Algebra 2

The vertices of a feasible region are A(1,2), B(5,2), C(1,4). Write a function that satisfies each equation. a) A is the maximum and B is the minimum. b) C is the maximum and B is the minimum. c) B is the maximum and A is the minimum.

34. ## maths

1. Prove using mathematical induction that 1+2+3+...+n=[ n(n+1)]/2 2. Find the derivative of 2^x^2+log2(2x^2-1) 3. Use DeMeoivre's theorem to simplify the following expressions [(Cos pie/3 + isin pie/3)^5 (cos 2pie/3- isin 2pie/3)^4]/ (cos pie/6 - isin

35. ## algebra(reiny)

Hey thanks for all your help but you kinda confused me on a few: 1)Determine whether f(x)=-5x^2-10x+6 has a maximum or minimum value and find that value A.minimum -1 B.maximum 11 C.maximum -1 D.minimum 11 and you said the function opens up, so there is a

Consider the following. f(x) = 8x (square root of (x − x^2)) (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.

Consider the following. f(x) = 8x(square root of (x − x^2)) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.

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

39. ## AP Calculus

Can someone check my answers: 1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { |x|, -2

40. ## Math

Football Lesson 5.1 1. y= -0.035x^2 + 1.4x + 1, where x is the distance (in yards) and y is the height (in yards) a. Does the graph open up or down? b. Does the graph have a Maximum value or a minimum value? c. graph the quadratic function. (i'll graph it

41. ## math pre calculus

find the following for the function f(x)=(x+5)^2(x-2)^2 a.find the x and y intercepts, b.find the power function that the graph ressembles for large values of x c.determine the maximum number of turning points on the graph of f d.determine the behavior of

42. ## Algebra2

Complete parts a – c for each quadratic function: a. Find the y-intercept, the equation of the axis of symmetry and the x- coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to graph the function. 1.

43. ## Absolute Extrema

Find the minimum and maximum values of the function f(x)= 2/3 sin pix on the interval [1,2] (domain). I got (1.5, -2/3) as the minimum and no maximum on the interval. Is it correct? Thank you.

44. ## Calculus

For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) Graph y = f_c(x) for these values of the parameter c: c = -1, 0, 1, 2, 3, 4. What are the similarities and differences among the graphs, and how do the graphs change as the parameter

45. ## Calculus

Use analytical methods to find the exact global maximum and minimum values of the function f(x)=8x-ln(4x) for x >0. If a global maximum or minimum does not exist, enter the word NONE. For the global maximum at x=none, But for the Global minimum at x=? Is

46. ## Help me check my calculus questions

Can someone check my answers: 1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { |x|, -2

47. ## trigo

find the period, amplitude,zeros, extreme points at maximum and minimum of the given function: 1.y = sin( -2x) 2.y = 4 sin( 5x) 3.y = -3 sin (3x/5) 4.y = 1/2 cos (-4x)

48. ## Calculus

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as a

49. ## Mathematics

Find the maximum or minimum values of sin x+sin y+sin(x+y)

50. ## Algebra

How do you figure out the minimum and maximum for the graph of a function (without having a list of data, just looking at the graph?) Would you right both of the minimums (there's two points that are equally low), one of them or do something different?

51. ## maths

1. Prove using mathematical induction that 1+2+3+...+n=[ n(n+1)]/2 2. Find the derivative of 2^x^2+log2(2x^2-1) 3. Use DeMeoivre's theorem to simplify the following expressions [(Cos pie/3 + isin pie/3)^5 (cos 2pie/3- isin 2pie/3)^4]/ (cos pie/6 - isin

52. ## Calculus

Use a graph or level curves to find the local maximum and minimum values and saddle points of the function. Then use calculus to find these values precisely. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)

53. ## MATH

The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D)

54. ## calculus

Consider the graph of the cosine function shown below. y=4 cos (2 x) a. Find the period and amplitude of the cosine function. b. At what values of θ for 0 ≤ θ ≤ 2π do the maximum value(s), minimum value(s), and zeros occur? so i don't know how to

55. ## math

1.How is the maximum or minimum point of the original quadratic function related to the maximum or minimum point of its reciprocal function? 2.How can you use the leading coefficient of the original quadratic function to tell you whether its reciprocal

56. ## Calculus (pleas help!!!)

Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum = Absolute minimum = (B)

57. ## math

Let g be a function that is defined for all x, x ≠ 2, such that g(3) = 4 and the derivative of g is g′(x)=(x^2–16)/(x−2) with x ≠ 2. Find all values of x where the graph of g has a critical value. For each critical value, state whether the graph

58. ## Physics ( Calculus & Mecahnics )

A proton with mass m moves in one dimension.The potential-energy function is where and are positive constants. The proton is released from rest a x0 = a/b. (a) Show that can be written as U(x) = a --- [ ( x0/x )^2 - x0/x ] x0^2 Graph U(x). Calculate U(x0)

59. ## Algebra

I frequently find myself lost with concepts in math, and even looking at some problems is an anxiety trip. I have several questions on a test, all vaguely revolving around the same concept, but I'm not sure how to make sense of them. Could someone explain

60. ## Calculus

Find the absolute maximum and absolute minimum values of the function f(x)=x^3+6x^2-63x+4 on each of the indicated variables. Enter DNE for does not exist. (A) Interval = [-8,0] Absolute maximum = Absolute minimum = (B) Interval = [-5,4] Absolute maximum =

61. ## AP CALC. AB

2. A cubic function is a polynomial of degree 3 and has the form y=mx^3+bx^2+cx+d; m≠0. What is the maximum quantity of local extreme values a given cubic function can have? a. 2 b. 1 c. 0 d. 3 Is it (a)?? 2. Let f(x)=xln(x). The minimum value attained

62. ## Calculus

Consider the function f(x)=sin(1/x) Find a sequence of x-values that approach 0 such that sin (1/x)=0 sin (1/x)=1 sin (1/x)=-1 Is sin sin (1/x)=0 and sin (1/x)=-1 does not exist. What is sin (1/x)=1 then. How would I show the sequence of values, any help

63. ## Calculus

Answer the following questions for the function f(x) = sin^2(x/3) defined on the interval [ -9.424778, 2.356194]. Rememer that you can enter pi for \pi as part of your answer. a.) f(x) is concave down on the interval . b.) A global minimum for this

64. ## algebra

find the vertex, the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=x^2-4x-5

65. ## MATH

The graph of a trigonometric function oscillates between y=1 and y=-7. It reaches its maximum at x= pi and its minimum at x=3pi. which of the following could be the equation of the function? A) f(x)=4 cos x/2-3 B) f(x)=4 sin x/2-3 C) f(x)=4 sin 2x-3 D)

66. ## calculus

there are no examples of this type of problem in my book so if you could help walk me through it - that would be extremely helpful. thanks ahead of time. Find the extreme values of the function on the interval and where they occur. 4) F(x)=³√(x); -3

67. ## Help me check my calc answers?

Can someone check my answers: 1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { |x|, -2

68. ## Calculus

For any constant c, define the function f_c(x)= x^3+2x^2+cx. (a) Graph y = f_c(x) for these values of the parameter c: c = -1, 0, 1, 2, 3, 4. What are the similarities and differences among the graphs, and how do the graphs change as the parameter

69. ## Math

The question is: Fr what value(s) of k will the function f(x)=(kx^2)-4x+k have no zeroes. So for that, the discriminant would be less than 0. 0>D 0>((-4)^2)-4(k)(k) 0>16-(4k^2) 4k^2>16 k^2>4 k>+2/-2 So I know that I'm supposed to graph it with D as one

70. ## how to sketch a graph of..

Local minimum and local maximum imply that the function approaches negative and positive infinite at opposite sides of the graph. Local minimum (1,1) and local maximum (3,3) means the slope of the function is 0 at these points. Thank you so much. So 1)when

71. ## Calculus I

Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. 18. f(x) = 1/x , 1 < x < 3 I can graph it just fine, but for my answer I got that the function has none of the above. Is this correct?

72. ## trig/precalc

a car's flywheel has a timing mark on it's outer edge. the height of the timing mark on the rotating flywheel is given by y=3.55sin[x - (pi/4)]. graph one full cycle of this function. I was not taught how to graph a function like this, only the simple y=

73. ## Algebra

Find the vertex, the line of symmetry, the maximum or minimum of the quadratic function, and graph the function. f(x)=x^2-4x-3 What is the vertex? (Type an ordered pair) What is the equation of the line of symmetry? x= What is the maximum/minimum of f(x)?

74. ## Calculus

How do I graph sin and cosin example: graph y=-4sin(x + 3.14) Your function is the sin function shifted by pi units to the left. You need to study the sin function and know how to graph it. There should be a picture of it in your text, it's a very commonly

75. ## Trignometry

Let m and M be the minimum and maximum values of the domain of f(x)=sin^−1(x2−35), respectively. What is the value of M−m? sin^-1 is sin inverse

76. ## Calculus (pleas help!!!)

Find the absolute maximum and absolute minimum values of the function f(x)=(x−2)(x−5)^3+11 on each of the indicated intervals. Enter -1000 for any absolute extrema that does not exist. (A) Interval = [1,4] Absolute maximum = Absolute minimum = (B)

77. ## Calc 3

Find the maximum and minimum values of the function f(x,y,z)=x+2y subject to the constraints y^2+z^2=225 and x+y+z=1. Maximum and minimum value is?

78. ## math

Maximum or minimum values of the function f(x) = (1 – x)^2 e^x is: i need solution (a) Minimum value at x = –1; maximum value x = 1 (b) Minimum value at x = 1; maximum value x = –2 (c) Minimum value at x = 1; maximum value x = –1 (d) None of these

79. ## one more graph question

Hopefull the last one. :) Sketch the graph of a differentiable function y = f(x) with this property: A local minimum value that is greater than one of its local maximum values

80. ## Algebra II repost- please check

I posted these a little while ago but this time I have answered them. 1. Does the graph of y = x – 3x2 + 5 have a maximum or minimum? 2. What is the vertex of the graph of y = -2(x - 3)2 + 4? 3. Does the graph of y = -2(x - 3)2+ 4 open up or down? My

81. ## Physics ( oscillations and waves)

two collinear harmonic oscillations are X1= 8 sin( 100pi *t) and X2= 12 sin(96 pi *t) are superposed. calculate the values of time when the amplitude of the resultant oscillation will be maximum and minimum

82. ## calculus

Find the absolute extrema of the function (if any exist) on each interval. (If an answer does not exist, enter DNE.) f(x) = square root of (25 − x^2) (a) [−5, 5] minimum (x, y) = (smaller x-value) (x, y) = (larger x-value) maximum (x, y) = (b) [−5,

83. ## precalculus

analyzethe graph of the function Find the x- and y-intercepts. (b) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (c) Find the maximum number of turning points. (d) Graph the function Please show

84. ## calculus

Give a reasonable sketch, on the axes provided, of the graph of the function x/(x^2-1)^1/2 showing all characteristics. Use the following pieces to justify your sketch. a) Domain ? b) coordinates x and y intercepts ? c) Symmetry ? is the function odd,

85. ## Maths

From looking at a periodic function, we had to decide on the equation for it. I got: y = 1.05 sin x2pi/11.72 + 1.55 1.05 is the 'a' value of the equation 2pi/11.72 is the 'b' value for the equation 1.55 is the 'd' value of the equation we were told not to

86. ## Math

Draw the Cartersian graph of Y=x^2+2x-3 for values of x range from -4 to +2.use the graph to find a) The value of Y when x=1.5 b) The value of x when Y =1 c) The maximum value of x^2+2-3 d) The minimum value of x^2+2-3 e) The root of the

87. ## Math

Use the given graph of the function on the interval (0,8] to answer the following questions. Where does the function f have a local maximum? Answer (separate by commas): x= Where does the function f have a local minimum? What is the global maximum of f?

88. ## math

find the vertex, the line of symmetry and the maximum or minimum value of f(x). graph the function. f(x)=-(x+6)^2-2 The vertex is The line of symmetry is x= The minimum/maximum value of f(x) is? The value of f(-6) =-2 is maximum or minimum? and the graph

89. ## algebra

Annual profit in thousands of dollars is given by the function,p(x)=200square x-3 +10,000,where x is the number of items sold in thousands, x less than 3. describe the meaning of the numbers 3 and 10,000 in the formula. find the profit for 5 different

90. ## Maths

Find the absolute maximum and minimum values of the function f (x) = [x^(2/3)]*[x − 1] on the closed interval [0, 4], and state where these values occur.

91. ## Algebra

1. To obtain the graph of y = asinb (x - h) + k , explain what each of the values of a, b, h, and k affects the graph of function y = sin x

92. ## Calculus

f(x) = sin^2(x/2) defined on the interval [ -5.683185, 1.270796]. Remember that you can enter pi for \pi as part of your answer. a.) f(x) is concave down on the interval . b.) A global minimum for this function occurs at . c.) A local maximum for this

93. ## Algebra 2

The vertices of a feasible region are A(1,2), B(5,2), C(1,40. Write a function that satisfies each equation. a) A is the maximum and B is the minimum. b) C is the maximum and B is the minimum. c) B is the maximum and A is the minimum.

94. ## math

Which three options are true about the quadratic equation?? y= 4t^2 + 16t + 18 A. The graph has a minimum. B. The graph of y crosses the horizontal axis at t = 10 and t = 20. C. The equation 4t^2 + 16 + 18 = 6 has one real solution. D. The function has a

95. ## algebra

Find the line of symmetry, the maximum or minimum value of the quadratic function, and graph the function f(x)=2-x^2

96. ## calc

How I can to determine the domain and the maximum and minimum local of the following function: f(x)=6sec((pi*x)/8). And I need to graph the function.

97. ## pre calculus

find the following for the function f(x)=(x+3)^2(x-1)^2 a.) find the x and y intercept of the polynomial function f. b.)find the power function that the graph of f ressembles for large values of lxl. c.)determine the maximum number of turning pointsof the

98. ## calculus

For what values of a and b does the function f(x)=ax^3+bx have a minimum or maximum at x=2?

99. ## maths

Which three options are true about the quadratic equation?? y= 4t^2 + 16t + 18 A. The graph has a minimum. B. The graph of y crosses the horizontal axis at t = 10 and t = 20. C. The equation 4t^2 + 16 + 18 = 6 has one real solution. D. The function has a

100. ## math

I need to use calculus to solve this word problem: Find all maximum and minimum values for f(x)= sin(x)+ cos(x) on [0, 2(3.14)] How do I do it?