The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?

46,066 results
  1. Calculus

    The line that is normal to the curve x^2=2xy-3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy - 3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 + 2xy - 3y2 = 0 ? I'll

  2. 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

  3. 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

  4. 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

  5. Calculus

    The curve y = x/(1 + x^2) is called a serpentine. Find an equation of the tangent line to this curve at the point(2, 0.40).(Round the slope and y-intercept to two decimal places.)

  6. 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!

  7. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?

  8. math

    Find the slope of the line tangent to the curve y=cos(2x) at the point where x=pi/6

  9. AP AB Calculus

    Linear approximation: Consider the curve defined by -8x^2 + 5xy + y^3 = -149 a. find dy/dx b. write an equation for the tangent line to the curve at the point (4,-1) c. There is a number k so that the point (4.2,k) is on the curve. Using the tangent line

  10. Math (Implicit Differention)

    use implicit differentiation to find the slope of the tangent line to the curve of x^2/3+y^2/3=4 at the point (-1,3sqrt3)

  11. Calc

    Find an equation of the curve whose tangent line has a slope of f'(x) =2x^-10/11, given that the point ​(-​1,-4​) is on the curve.

  12. calculus

    Find the slope of the tangent line to the given polar curve at the point specified by the value of θ. r=6/θ, θ=π

  13. 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

  14. 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

  15. Calculus

    At what point on the curve x = 3t^2 + 2, y=t^3-8 does the tangent line have slope 1/2?

  16. calculus ap

    what is the slope of the line tangent to the curve y^3+x^2y^2-3x^3=9 at the point (1,2)?

  17. Calculus

    Find the equation of the line that is tangent to the curve x(t) = t^2+1 and y(t)=t^3-1 at the point (5,7). I get a slope of 7.5.

  18. calculus

    The point P(7, −4) lies on the curve y = 4/(6 − x). (a) If Q is the point (x, 4/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 6.9 mPQ = (ii) 6.99 mPQ =

  19. 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)

  20. 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

  21. 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

  22. please 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.

  23. Math

    The point P(8, −3) lies on the curve y = 3/(7 − x). (a) If Q is the point x, 3/(7 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 7.9 mPQ = (ii) 7.99 mPQ =

  24. Calculus: for mathmate

    Find the slope of the tangent line to the graph of the given function at any point: 1. f(x)= 13 I understand that you said the tangent to the line is the coefficient of x, but what would be the slope of this problem. For problems like this are there

  25. 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

  26. Calc :(((((

    The curve y = x/(1 + x^2)is called a serpentine. Find an equation of the tangent line to this curve at the point (4, 0.24). Round the slope and y-intercept to two decimal places.)

  27. calculus

    To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (64, 8), we know that (64, 8) is a point on the line. So we just need to find its slope. The

  28. calculus

    Find the equation of the tangent line to the curve y=sqrt(x) at x = c. Put the answer in slope intercept form y=mx+b. Use the definition of the slope of the tangent with no short cuts.

  29. Calculus

    Find the slope of the tangent line to the curve (a lemniscate) 2(x^2+y^2)^2 = 25(x^2-y^2) at point (-3,-1).

  30. Calculus [finding slope of tangent line]

    Find the slope of the tangent line to the curve 0x^2−2xy+2y^3=10 at point (-4,1) Help please? Thanks in advance

  31. calculus BC slope

    consider the curve in xy-plane by x=e^t and y=te^(-t) for t is greater or equal to o. the slope of the line tangent to the curve at the point where x=3. all the answer choices are decimal points. a is 20.086, b is .342, c is -.005, d is -.011 and e is

  32. calculus

    Find the slope of the tangent line to the curve (sqrt(4x+y))+(sqrt(3xy)) at the point (3,4) The slope of the tangent line to the curve at the given point is ? I got -((1/2)+4sqrt(36))/((1/8)+3sqrt(36))

  33. 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.

  34. 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

  35. Calculus- Tangent Line

    What is the slope of the tangent line to the curve at the point (4, 0)? Okay, so I got 0.5, did I do this right?

  36. calculus - please help!

    Find the slope of the tangent line to the curve (3x+3y−27)^(1/2)+(2xy−39)^(1/2)=8 at the point (8,4).

  37. 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

  38. College Calculus

    Let f(x) = 3x^2 - 2x + 1 a) write an equation of the line going through the points (1, f(1)), and (2, f(2)). b) Find a point on the graph of f where the tangent line to the graph has the same slope as the line in part (a). Write the equation of the tangent

  39. Math (Calculus)

    Use implicit differentiation to find the slope of the tangent line to the curve y/(x–9y)=x^6–2 at the point (1,-1/-8). Can someone please help me? I don't understand

  40. 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

  41. 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.

  42. 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

  43. 12th Grade Calculus

    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

  44. 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.

  45. 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

  46. 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

  47. 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

  48. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (3, 1) is a point on the curve? A. x^2 + y^2 =8

  49. 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

  50. 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

  51. 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

  52. 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

  53. 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

  54. math

    consider the curve defined by the equation y=a(x^2)+bx+c. Take a point(h,k) on the curve. use Wallis's method of tangents to show that the slope of the line tangent to this curve at the point(h,k) will be m= 2ah+b. have to prove this for tow cases: a>0 and

  55. 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

  56. 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

  57. Calculus

    the slope of the tangent line to the curve y=(3/x) at the point (6,0.5000) is? the equation of this tangent line can be written in the form y=mx+b where m is? and where b is?

  58. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? x2 − y2 = 15 x2 + y2 = 15 x + y = 15

  59. calc

    The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (3, 1) is a point on the curve?

  60. 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

  61. Calculus 251

    The slope of the tangent line to the curve y= 3x^3 at the point (-1,-3) is:? The equation of this tangent line can be written in the form y=mx+b where m is:? and where b is:?

  62. Calc

    The slope of the tangent line to a curve is given by f'(x)=4x^2 + 7x -9. If the point ​(0,6​) is on the​ curve, find an equation of the curve.

  63. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? x2 − y2 = 15 x2 + y2 = 15 x + y = 15 xy = 15

  64. Calculus

    The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve? a) x^2-y^2=15 b) x^2+y^2=15 c) x+y=15 d) xy=15

  65. math calc. asap asap please

    the point on the curve is 4y=x^2 nearest to (7,2) is: this is what i did: i solved for y and I know that the there's a tangent line at (x1,y1). so using y-y1=m(x-x1), I found the lines of the tangent and perpendicual lines: slope is derivative so it is

  66. Math

    Use a formula for slope of a line tangent to a parametric curve to find dy/dx for the curve c(s) = (s^(-1)-6s, -7s^3) at the point with s=-4

  67. Math

    Use the formula for slope of a line tangent to a parametric curve to find dy/dx for the curve c(s) = (s^-1-6s, -7s^3) at the point with s=-4

  68. Math

    Suppose f(x)=5/(x-2). f'(5)=-5/9. Use this to find the equation of the tangent line to the curve y=5/x-2 at the point (5,(5/3)). write your answer in the form y=mx+b where m is the slope and b is the y-intercept. The equation of the tangent line is.....

  69. calc

    Find an equation of the tangent line to the curve at the given point. y = 6 x sin x P= (pi/2 , 3pi) i know the slope of a tangent line is equal to the first derivative. For that I got 6xcosx + 6sinx but idk how to put that into the y-y1=m(x-x1) formula to

  70. Chris

    The curve y = x/(1 + x^2) is called a serpentine. Find an equation of the tangent line to this curve at the point (2, 0.40). (Round the slope and y-intercept to two decimal places.)

  71. Calculus

    I could really use the help on this as soon as possible. what is the slope of the line tangent to the curve (/x)^2 at point (4,16)

  72. Calculus

    The slope of the line tangent to the curve xy+(y+1)^2=6 at the point (2, 1) is

  73. Calculus

    Find the slope of the tangent line to the curve 2(x^2 + y^2)^2 = 25(x^2 - y^2) at the point (3,1). Thank you very much for your help.

  74. Math

    Determine the slope of the tangent line to the curve y=2x^3-3x^2+1 at the point (1,0)

  75. Calculus

    Determine the slope of the tangent line to the curve y=2x^3-3x^2+1 at the point (1,0)

  76. Calculus

    what is the slope of the line tangent to the curve (/x)^2 at point (4,16) * (/x)= the squareroot of x

  77. Math

    Determine the slope of the tangent line to the curve y=2x^3-3x^2+1 at the point (1,0)

  78. calculus

    Find the slope of the tangent line to the curve x^2+y^3=5x^2y+5 at the point (1,−1). Please help!

  79. 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

  80. Calculus - Damon

    Find the line which passes through the point (0, 1/4) and is tangent to the curve y=x^3 at some point. So I found the derivative which is 3x^2. Let (a, a3) be the point of tangency. 3x^2 = (a3 - 1/4)/(a-0) I'm not sure how to solve for a. Yes, the point is

  81. calculus

    Find the slope of the tangent line to the curve (2x+4y)^1/2+(2xy)^1/2=13.4 at the point (6,5).

  82. calculus

    a.Find the slope of the tangent line to the curve y=9-2x^2 at the point (2,1) b.Find an equation of this tangent line.

  83. 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

  84. Calculus Help Please!!!

    Find the equation in slope intercept form of the tangent line and the normal line to the curve x^2+4xy+y^2=13 at the point.(2,1). show steps please!!! thank you!

  85. calculus

    Use implicit differentiation to find the slope of the tangent line to the curve (y/x+8y)=x^8 +9 at the point (1,10/-79).

  86. Math

    Use implicit differentiation to find the slope of the tangent line to the curve y/( x + 4 y) = x^4 – 4 at the point (1,-3/13)

  87. Calculus

    (y/(x+9y))= (x^2)-7 at the point (1, -6/55) Use implicit differentiation to find the slope of the tangent line to the curve

  88. Math

    Use implicit differentiation to find the slope of the tangent line to the curve y/( x + 4 y) = x^4 – 4 at the point (1,-3/13)

  89. math

    use implicit differentiation to find the slope of the tangent line to the curve (y)/(x-7y)=x^6+5 at the point (1,6/43)

  90. CAL

    use implicit differentiation to find the slope of the tangent line to the curve (y)/(x-7y)=x^6+5 at the point (1,6/43)

  91. Math

    Find the slope of the tangent line to the curve 0x^2−2xy+2y^3=10 at point (-4,1) Help please? Thanks in advance

  92. Calculus ap

    Use implicit differentiation to find the slope of the tangent line to the curve XY^3 + XY = 5 at the point (3,2) .

  93. Calc I

    Find an equation of the tangent to the curve at the given point. y=4(sinx)^2 point: pi/6,1) So I took the derivative of the original function to get: y' = 8cosx*sinx I then chose a point to plug in to find a point for the slope. i picked pi/6 because i

  94. Calculus

    Use implicit differentiation to find the slope of the tangent line to the curve –2x^2–2xy–1y^3=–3 at the point (–1–1).

  95. Rodriguez

    use implicit differentiation to find the slope of the tangent line to the curve of x^2/3+y^2/3=4 at the point (-1,3sqrt3)

  96. 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

  97. Calculus AP need help!

    i don't know how or what to starts Find the slope of the tangent line to the curve 4x^2+3xy+3y^3=-251 at the point (-4,-5)

  98. calculus

    Gah. Struggling over this for the past 20 minutes... Find the slope of the line tangent to the curve y=1/x at the point (2,0.5).

  99. Calculus AP

    implicit differentiation Find the slope of the tangent line to the curve xy^3 + 2y - 0.76 =0 at the point (-3, o.7) I'm lost. so 3xy^2 * y' + 2y = 0 right?

  100. 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

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