# Determine the points on the curve y=x^2(x^3-x)^2 where the tangent line is horizontal. Thx!

62,353 results
1. ## Calculus 1

Find the equation of the tangent line to the curve y = (9 ln x)/x at the points (1, 0) and (e, 9/e).

2. ## calculus

a) If x3 + y3 - xy2 = 5, find dy/dx. (b) Using your answer to part (a), make a table of approximate y-values of points on the curve near x = 1, y = 2. Include x = 0.96, 0.98, 1, 1.02, 1.04. (c) Find the y-value for x = 0.96 by substituting x = 0.96 in the

3. ## calculus

1. Given the curve a. Find an expression for the slope of the curve at any point (x, y) on the curve. b. Write an equation for the line tangent to the curve at the point (2, 1) c. Find the coordinates of all other points on this curve with slope equal to

4. ## calculus

Notice that the curve given by the parametric equations x=25−t^2 y=t^3−16t is symmetric about the x-axis. (If t gives us the point (x,y),then −t will give (x,−y)). At which x value is the tangent to this curve horizontal? x = ? At which t value is

5. ## calculus

Find the points on the curve y = 2x^3 + 3x^2 - 12x + 1 where the tangent is horizontal

6. ## AP Calc. AB

At how many points on the curve y=4x^5-3x^4+15x^2+6 will the line tangent to the curve pass through the origin?

7. ## math

Consider the equation x^2y+3y^3=24 Find dy/dx I got -2xy/x^2+9y^2 The next question is Determine the points, if any where the tangent line to the graph of the equation is horizontal How do I do this part??

8. ## last calc question, i promise!

given the curve x + xy + 2y^2 = 6... a. find an expression for the slope of the curve. i got (-1-y)/(x + 4y) as my answer. b. write an equation for the line tangent to the curve at the point (2,1). i got y = (-1/3)x + (5/3). but i didn't any answer for c!

9. ## Calculus

Consider the curve given by y^2 = 2+xy (a) show that dy/dx= y/(2y-x) (b) Find all points (x,y) on the curve where the line tangent to the curve has slope 1/2. (c) Show that there are now points (x,y) on the curve where the line tangent to the curve is

10. ## calculus

Determine the points in the interval (0, 2π) at which the graph of the function below has a horizontal tangent line. f(x) = 10 cos x + 5 sin 2x There should be three

11. ## Calculus

1. On what interval is the function f(x)=x^3-4x^2+5x concave upward? 2. For what values of x dies the graph of f(x)=2x^3-3x^2-6x+87 have a horizontal tangent? Is there no solution because the equation can't be factored? 3. At what point on the curve

12. ## Math

The line has equation y=2x+c and a curve has equation y=8-2x-x^2. 1) for the case where the line is a tangent to the curve, find the value of the constant c. 2) For the case where c = 11, find the x-coordinates of the points of intersection of the line and

13. ## Math (Calculus) (mean value theorem emergency)

Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c in the interval (-2,4)

14. ## Calculus

A) The point p(3,1) lies on the curve y= square root x-2. If Q is the point (x, square root x-2) use your calculator to find the slope of the decant line PQ for the following values of x 1) 2.5 2.) 2.9 3.) 2.99 4.) 2.999 5.) 3.5 6.) 3.1 7.) 3.01 8.) 3.001

15. ## calculus

Find the x-coordinates of all points on the curve f(x) = sin 2x − 2 sin x at which the tangent line is horizontal. (Enter your answers as a comma-separated list. Use n to represent any integer.)

16. ## math

For the curve given by 4x^2+y^2=48+2xy, show that there is a point P with x-coordinate 2 at which the line tangent to the curve at P is horizontal.

17. ## calculus

Consider the curve defined by 2y^3+6X^2(y)- 12x^2 +6y=1 . a. Show that dy/dx= (4x-2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope -1 is tangent to the curve at point P. Find the

18. ## Calculus

a)The curve with equation: 2y^3 + y^2 - y^5 = x^4 - 2x^3 + x^2 has been linked to a bouncing wagon. Use a computer algebra system to graph this curve and discover why. b)At how many points does this curve have horizontal tangent lines? Find the

19. ## calculus 1

The point P(2,-1) lies on the curve y=1/(1-x) If Q is the point (x, 1/(1-x) find slope of secant line. these are the points 2, -1 1.5,2 1.9,1.111111 1.99,1.010101 1.999,001001 2.5,0.666667 2.1,0.909091 2.01,0.990099 2.001,0.999001 using the results from

20. ## Calc AB

Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then: (Points : 1) A) The slope of the tangent line to the curve y = f –1(x) at

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P.

22. ## Calculus

at what point is the tangent to f(x)=x^2+4x-1 horizontal? That would be when the derivative, df/dx = 2x + 4, equals zero. df/dx at any point of a curve f(x) is the slope of the tangent line.

23. ## Calculus

Consider the curve y^2+xy+x^2=15. What is dy/dx? Find the two points on the curve where y equals 0 and show that the tangent lines there are parallel. Find the coordinates of all points on the curve where there is a horizontal tangent line, with work.

24. ## calculus

1. Consider the function f(x) = X^(4/3) +4x^(1/3) on the interval -8 ≤ x ≤ 8. a. Find the coordinate of all points at which the tangent to the curve is a horizontal line. b. Find the coordinate s of all points at which the tangent to the curve is a

25. ## calc

Suppose a curve is traced by the parametric equations x=1sin(t) y=18-3cos^2(t)-4sin(t) At what point (x,y) on this curve is the tangent line horizontal?

26. ## calculus

Find all points on the curve x^2y^2+xy=2 where the slope of tangent line is -1. This is what I got. x^2y^2+xy=2 x^2*2ydy/dx + 2x*y^2 + x*dy/dx + y =0 dy/dx(2yx^2+x)= -2xy^2-y dy/dx = (-2xy^2-y)/(x+2yx^2) how do I finish from here? I need to know where the

27. ## Calculus

the curve: (x)(y^2)-(x^3)(y)=6 (dy/dx)=(3(x^2)y-(y^2))/(2xy-(x^3)) a) find all points on the curve whose x-coordinate is 1 and write an equation for the tangent line of each of these points b)find the x-coordinate of each point on the curve where the

28. ## calculus

Determine equations for the tangents to the points on the curve y = -x^4 + 8x^2 such that the tangent lines are perpendicular to the line x = 1. I've found the derivative, but not really sure where to go from here.

29. ## Calculus

Suppose that y=f(x) = sqrt(2x), x>=0 Find a c > 0 such that the tangent line to the curve y = f(x) at x = c has the same slope as the tangent line to the curve y = f^–1(x) at x = c. You get: c = 1/8 c = 1/2 c = (1/8)^(1/3) c = (1/3)^(2/3) c = (1/2)^(1/3)

30. ## Need help fast on calc

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P. -when plugging y as

31. ## Math- Calc 1

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (-1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he

32. ## Calculus

For the parametric curve defined x=2t^3-12t^2-30t+9 and y=t^2-4t+6 ..find dy/dx and then where is the tangent to the curve vertical (give the cartesian coordiantes of the points. and find the tang. to the curve horizontal dx/dt= 6t^2-24t-30 dy/dt= 2t-4

33. ## Calculus

At what points on the curve y=(x^2)/(2x+5) is the tangent line horizontal? y'=[(2x)(2x+5)-(2)(x^2)]/(2x+5)^2 =[2x^2+10x]/(2x+5)^2 I plugged 0 into x, and got the coordinates (0,0). How do I get the other pair of coordinates? Thanks in advance.

1. a.) Find an equation for the line perpendicular to the tangent curve y=x^3 - 9x + 5 at the point (3,5) [* for a. the answer that I obtained was y-5 = -1/18 (x-3) ] b.) What is the smallest slope on the curve? At what point on the curve does the curve

35. ## math

L is a straight line in x-y plane. its equation is in the form y-8=m(x-1) determine all points in x-y plane where line L intersects curve y=2x^2 i know that 1,8 is a point on the line. I'm not sure what points the question is looking for here. Without

36. ## Calculus

Determine an equation of the tangent line to the curve of f (x) = 3e^4x − 3 at the point where the curve crosses the y-axis.

37. ## calculus

Find the points on the curve y= 2x^3 + 3x^2 - 36x + 7 where the tangent is horizontal.

38. ## Calculus

1) An equation of the line contains points (7/9, 7) and (-7/9) is 2) Find the slope of the line tangent to the curve y=x^2 at the point (-0.6, 0.36) and find the corresponding equation of the tangent line

39. ## calculus help

Find the points where the tangent line is horizontal or vertical. Find the area under one period of the curve. x= r(deta - cos deta) Y= r(1- sin deta)

40. ## Math (Calculus)

Consider the curve represented by the parametric equations x(t)= 2+sin(t) and y(t)=1-cos(t) when answering the following questions. A) Find Dy/Dx in terms of t I got tan(t) B) Find all values of t where the curve has a horizontal tangent. I got (+-)(pi)(n)

41. ## Calculus

I found part B, but stuck on part A. Use implicit differentiation to find the points where the parabola defined by x^2-2xy+y^2+4x-8y+24= 0 has horizontal and vertical tangent lines. A) The parabola has horizontal tangent lines at the point(s): B)The

42. ## math

1 A particle is moving in a stright line with the position at any time t is given by s= t³–9t²+3t+1,where s in meters and t in second. Find its position and acceleration when velocity is ¯24m/s 2. Given that x²cos y_sin y=0,(0,π). A. Verify that the

43. ## math

Determine the points on the curve y=x^2(x^3-x)^2 where the tangent line is horizontal. Thx!

44. ## Calculus AB

Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is no point on the graph of

45. ## Calculus

Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write an equation for the

46. ## Calculus

Use the given equation to answer the following questions. (Enter your answers from smallest to largest.) r = 8cos(¦È) 0 ¡Ü ¦È < ¦Ð (a) Find the points on the given curve where the tangent line is horizontal. theta= theta= (b) Find the points on the

47. ## calculus

1. Consider the function f(x) = X^(4/3) +4x^(1/3) on the interval -8 ≤ x ≤ 8. a. Find the coordinate of all points at which the tangent to the curve is a horizontal line. b. Find the coordinate s of all points at which the tangent to the curve is a

48. ## calculus

Given the curve defined by the equation y=cos^2(x) + sqrt(2)* sin(x) with domain (0,pi) , find all points on the curve where the tangent line to the curve is horizontal

49. ## Help Calc.!

original curve: 2y^3+6(x^2)y-12x^2+6y=1 dy/dx=(4x-2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point P.

50. ## Math

How can I determine a value of gradient from a graph if the line is curved. (not a straight line) This is where Calculus comes in If a graph is a curve, then the gradient (slope) of the curve is the slope of the tangent that you draw at a particular point

51. ## Calculus

Can someone show how this question is solved. Consider the curve given by the equation 2y^3 + y^2 - y^5 = x^4 -2x^3 +x^2 Find all points at which the tangent line to the curve is horizontal or vertical. Thanks!

use the derivative of f(x)=2x^3 + 6x to determine any points on the graph of f(x) at which the tangent line is horizontal a. (1,8) and (-1,-8) b. f(x) has no points with a horizontal tangent line c. (2,28) and (-2,28) d. (1,8) e. (0,0)

53. ## Calculus

Find all points on the curve where the tangent line is horizontal y = (x^6/6) - (x^2/2) + 1

54. ## math

question: find the points at which the graph of x^2 -4x + y62 -6y =12 has a vertical or horizontal tangent line. I found the deriviative to be (x-2)/(3-y) Then, the x value for a horizontal would be x=2 and the y value for a vertical would be y=3. But how

55. ## Math- Calc 1

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (1,1) intersect the curve again? 2. Find the constants A, B so that if Y = Asin X = B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points om he

56. ## Calc

1. At what point does the normal line to the curve x^2 - XY + Y^2 = 3 at the point (-1,1) intersect the curve again? 2. Find the constants A, B so that if Y=A*sin X + B cos X, then Y satisfies the differential equation Y" + 2Y = 0. 3. Find the points on he

57. ## Math - Tangent of a line

Determine the point on the curve y=x^2(x^3-x)^2 where the tangent line is horizontal.

58. ## Calculus

There are two neighboring points P and Q on the curve f(x)=x^2 (a) Determine m(h), the slope of the straight line PQ (b) The slope, S, of the tangent at P is defined as S=lim h->0 m(h). Find the value of S. (c) Use this value of S to show that the equation

59. ## maths

Find the x-coordinates of all points on the curve y=2sin-sin^2x at which the tangent line is horizontal.

60. ## Calculus

I have a two part question that pertains to a curve (r(x)) and its tangent line at x=3. We are given that at x=3, r(x)=8. In order to find the slope of the tangent line, we are given another point (on the tangent line): (3.2, 8.5). Therefore the slope of

61. ## Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive? Negative? Zero? 2) Find an equation of the tangent line to the oven curve at the specified point.

62. ## calculus

the tangent line to the curve y=1/3(x^3)-3x^2+11x+15 is parallel to the line 9x-3y=2 at two points on the curve.Find the two points.

63. ## calculus

dy/dx= (2x-2xy)/(x^2+2y) Find all points on the curve where x=2. Show there is a horizontal tangent to the curve at one of those points.

64. ## calculus

dy/dx= (2x-2xy)/(x^2+2y) Find all points on the curve where x=2. Show there is a horizontal tangent to the curve at one of those points.

65. ## calculus

dy/dx= (2x-2xy)/(x^2+2y) find all points on the curve where x=2. show there is a horizontal tangent to the curve at one of those points.

66. ## calculus

x^2-x^2y=y^2-1 find all points on the curve where x=2. Show there is a horizontal tangent to the curve at one of the points.

67. ## Math

In this problem we consider drawing some straight lines which form a nice pattern. Consider joining the point (0.1,0) to the point (0,0.9) by a line segment; then joining (0.2,0) to (0,0.8) by a line segment; and so on. In general, consider joining the

68. ## calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2 + 1 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent point is far from the

69. ## pre calc

Use the derivative of f(x) = 6x7 + 7x6 to determine any points on the graph of f(x) at which the tangent line is horizontal.

70. ## Precalc

Find the derivative of: f(x) = 1/(3x)^4 + 3x^4 Determine the points, if any, at which the function has a horizontal tangent line y = 5x^3 - 15x^2 y = 2x^3 + 6x^2 thank you!

71. ## Calculus

If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x + . Check your answer for

72. ## Calculus

Given the function y=(x^2-5/x+3), answer the following questions. a) Find dy/dx. Simplify your answer b) Find the coordinates of any points on the graph of y where the tangent line is horizontal. Show your work. c) Are there any points on the graph of y

73. ## calc

for the parametric curve defined by x=3-2t^2 and y=5-2t ...sketch the curve using the parametric equation to plot of the point. use an arrow to indicate the direction of the curve for o

74. ## calculus

find the x-coordinate of all points on the curve y=12Xcos(5X)-(30*sqrt3*X^2) + 16, pi/5

75. ## Calculus

Consider line segments which are tangent to a point on the right half (x>0) of the curve y = x^2+7 and connect the tangent point to the x-axis. If the tangent point is close to the y-axis, the line segment is long. If the tangent point is far from the

76. ## Calc.

Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph, and shade the area under

77. ## Calc.

sketch the curve using the parametric equation to plot the points. use an arrow to indicate the direction the curve is traced as t increases. Find the lenghth of the curve for o

78. ## Calculus

55. Find an equation of the tangent line to the graph of f(x) =x^3 - 2x + 1 a) at (2,5); b) at (-1,2); c) at (0,1). I believe the answers are: a) y= (3/2 x) - (3/2) b) No solution c) No solution For each function, find the points on the graph at which the

79. ## math

The equation of a curve is y = x^3 + x^2 - x -1 (a) Determine: (i) the stationary points of the curve; (ii) the nature of the stationary points in (a)(i) above. (b) Determine: (i) the equation of the tangent to the curve at x = 1; (ii) the equation of the

80. ## Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is a good approxiamtion to

81. ## Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is a good approxiamtion to

82. ## Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is a good approxiamtion to

83. ## Calculus

Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is a good approxiamtion to

84. ## calculus

find the points on the curve y=2x^3+3x^2-12x+1 where tangent is horizontal.

85. ## calculus

find an equation of the tangent line to the curve at the given point. graph the curve and the tangent line y=x/x-1 at (2,2) )

86. ## calculus

Find the points on the curve y=(cosx)/(2+sinx) at which the tangent is horizontal.

87. ## Calculus - Tangent Line

Hi, im having problems with the following problem. The main issue is actually starting the problem. Find the two points on the curve y = x^4 - 2x^2 - x that have a common tangent line. First, find the derivative of y(x) so that you know the slope of the

88. ## Calculus

Find an equation of the tangent line to the curve f(x)=-1/x+2 at the points (2, -1/4).

89. ## Maths

I need some help with my maths questions please! What angle does the tangent to the curve y=x^4-x^3+7x make with the positive direction of the x-axis at the point where x=2? Find any x values for which the gradient of the tangent to the curve y=x^2-3x-1 is

90. ## calculus

let x^2 + 4xy + y^2 + 3 = 0 are there any points on the curve where the tangent is horizontal or vertical? justify your answer.

91. ## calc

determine the x-coordinate of the point on the curve y=2x(lnx) at which the tangent line is parallel to the line y=4x+9

92. ## Calculus

Determine the equation of the line perpendicular to the tangent line to the function f(x) = 1/2 (e^x)at the point on the curve where x=ln3.

93. ## Calc

1. Differentiae each function a) Y=-3x^2+5x-4 b) F(x) = 6/x-3/x^2 c) F(x)=(3x^2-4x)(x^3+1) 2. Determine the equation of the tangent line to the curve y=2x^2-1 at the point where x=-2 3. Evaluate, rounding to two decimal places, If necessary a) In 5 b) b)

94. ## Math

Consider the curve represented by the parametric equations x(t)= 2+sin(t) and y(t)=1-cos(t) when answering the following questions. A) Find Dy/Dx in terms of t B) Find all values of t where the curve has a horizontal tangent. C) Find all values of t where

95. ## Math

Consider the curve represented by the parametric equations x(t)= 2+sin(t) and y(t)=1-cos(t) when answering the following questions. A) Find Dy/Dx in terms of t B) Find all values of t where the curve has a horizontal tangent. C) Find all values of t where

96. ## calculus

how would i go about finding the tangent line to the curve of sqrt(1+4x^2y^2)-3xy=-18 with the points (3,6)?

97. ## maths

In a reference (O, i, j), the points A (-12, 1150) and B (10, -500). The function f is defined on (-20, 10) by: f(x) = x^ 4 +2.25 x^3-44.5x^2-260x+100 We note Cf his(her,its) representative curve. We try to determine all the points of intersection of the

98. ## math

In a reference (O, i, j), the points A (-12, 1150) and B (10, -500). The function f is defined on (-20, 10) by: f(x) = x^ 4 +2.25 x^3-44.5x^2-260x+100 We note Cf his(her,its) representative curve. We try to determine all the points of intersection of the

99. ## Calculus HELP

Determine where (x-value only) on the curve y=1/(2x−1)^2 where the tangent line will be perpendicular to the line defined by 2x+y−1=0. we haven't learned this in the curriculum so damon i would love your help rn

100. ## calculus

find a point on the curve x^3 + y^3 =2xy other than the origin at which tangent line is horizontal