Consider the parabola y = 6x − x2. (a) Find the slope of the tangent line to the parabola at the point (1, 5). 4 (b) Find an equation of the tangent line in part (a). y =

112,394 results
  1. Calc 2

    Find the area of the region bounded by the parabola y = 5x2, the tangent line to this parabola at (5, 125), and the x-axis. its not 625/3

  2. 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

  3. calculus 2

    Find the area of the region bounded by the parabola y = 3x^2, the tangent line to this parabola at (1, 3), and the x-axis.

  4. Calculus (pleas help!)

    Find the slope of the tangent line to the ellipse x^2/36 + y^2/49 =1 at the point (x,y). slope =_______ Are there any points where the slope is not defined? (Enter them as comma-separated ordered-pairs, e.g., (1,3), (-2,5). Enter none if there are no such

  5. math

    Draw a diagram to show that there are two tangent lines to the parabola y = x2 that pass through the point (0, −25). Find the coordinates of the points where these tangent lines intersect the parabola.

  6. 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

  7. 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 =

  8. math

    graph the line with slope 1/2 passing through the point(-5,-2) find the slope of the line 5x+5y=3 write answer in simplest from consider the line 2x-4y=4 what is the slope of a line perpendicular to this line. what jis the slope of a line parallel to this

  9. 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

  10. calculous

    Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.

  11. math

    Consider the parabola y = 6x − x2. (a) Find the slope of the tangent line to the parabola at the point (1, 5). 4 (b) Find an equation of the tangent line in part (a). y =

  12. clculus

    find the parametric equation of the line that is tangent to the parabola y=x^2 at the point(-2 , 4)

  13. math

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=7x-5x^2 at (-2,-34) m = ?? y = ?? .

  14. calculus 2

    Find the area of the region bounded by the parabola y = 5x^2, the tangent line to this parabola at (3, 45), and the x-axis.

  15. Math

    Find the equation of the line tangent to curve x=sec(t), y=tan(t), at t=pi/6. I found th slope(derivative of the two which was csc(t). Plugged in Pi/6 and got 2 as the slope. Now how do I find the equation of the tangent? There are like two equations to

  16. Math

    Consider the graph of the parabola ​f(x)equals=x squaredx2. For xgreater than>0 and hgreater than>​0, the secant line through​ (x,f(x)) and ​(xplus+​h,f(x+h)) always has a greater slope than the tangent line at​ (x,f(x)). Choose the correct

  17. Calculus

    1. use the definition mtan=(f(x)-f(x))/(x-a) to find the SLOPE of the line tangent to the graph of f at P. 2. Determine an equation of the tangent line at P. 3. Given 1 & 2, how would I plot the graph of f and the tangent line at P if : f(x)=x^2 +4,

  18. 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.

  19. 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

  20. 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

  21. Calculus

    Draw a diagram to show that there are two tangent lines to the parabola y=x^2 that pass through the point (0,-4). Find the coordinates of the points where these tangent lines intersect the parabola. So far I have taken the derivative and got y'=2x.. Using

  22. Math - point on the graph (check +help)

    Determine the coordinates of the point on the graph of f(x)=sqrt(2x+1) where the tangent line is perpendicular to the line 3x+y+4=0 I do not seem to get the answer... I find the first derivative of f(x0 and equate it to the value of the slope from the

  23. calculusiii

    he paraboloid z = 4 − x − x2 − 2y2 intersects the plane x = 4 in a parabola. Find parametric equations in terms of t for the tangent line to this parabola at the point (4, 2, −24). (Enter your answer as a comma-separated list of equations. Let x,

  24. calculus

    The slope of the tangent line to the parabola y=4x2–6x+6 at the point where x=5 is: The equation of this tangent line can be written in the form y=mx+b where m is: and where b is:

  25. math help

    find the equation to the tangent line of the parabola given by x^2=2y at point (3, 9/2)

  26. 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 =

  27. calculus

    The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at point P and the parabola y=4x^(2)+4x+5 at point Q. a. If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point Q, find the value of c where c>0.

  28. math

    The line x=c where c>0 intersects the cubic y=2x^(3)+3x^(2)-9 at point P and the parabola y=4x^(2)+4x+5 at point Q. a. If a line tangent to the cubic at point P is parallel to the line tangent to the parabola at point Q, find the value of c where c>0.

  29. 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

  30. Calc

    The slope of the tangent line to the parabola y=4x2–3x+5 at the point where x=–5 is: (-43) The equation of this tangent line can be written in the form y=mx+b where m is: (-43) and where b is:_____________?

  31. calculus

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8

  32. mathematics

    Find the slope of the tangent line to the curve below at the point ( 5 , 5 ) . √3x+2y+√4xy=15 slope=

  33. calculus

    The slope of the tangent line to the parabola y=3x^2+6x+5 at the point (-3,14)

  34. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/4 x at (1,15/4)

  35. maths

    Find parametric equations of the line that is tangent to the parabola y = x^2 at the point (−2, 4).

  36. maths

    find the gradient of the tangent to the parabola y=4x-x^2 at (0,0) hence calculate the size of the angle between the line y=x and this tangent. (as i cant show you the diagram all that it shows is the line going through (0,0) and having one point of

  37. calculus

    Find the area of the region bounded by the parabola y=x^2 , the tangent line to this parabola at (10, 100), and the x-axis.

  38. 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

  39. 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.

  40. Mathematics

    Use implicit differentiation to find the points where the parabola defined by x2−2xy+y2−4y+4=0 has horizontal and vertical tangent lines. The parabola has horizontal tangent lines at the point(s) (x-y)/x-y+2 . The parabola has vertical tangent lines at

  41. 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

  42. calc

    The slope of the tangent line to the parabola y=4x2–3x+5 at the point where x=–5 is:______ The equation of this tangent line can be written in the form y=mx+b where m is:_________ and where b is:______? The first to blanks are -43, but what is b?

  43. 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

  44. Math

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 9/(5 x) ( at ) \(1,(9/5)) m = y=

  45. Math (Calculus 121)

    The derivative tells you the slope at any point. df/dx = 8 x^3 - 12 x When x = 3, the slope is m = 8*27 - 36 = 180 and the equation of the tangent line is (y - 228) = 180*(x - 3) y = 180 x - 540 + 228 = 180 x - 312 wow, that was absolutely correct (i just

  46. 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

  47. Calculus

    Find the slope of a line tangent to the curve y=2x^2+4x at the point P(−3,6) by finding the limit of the slopes of the secant lines PQ where Q has​ x-values −2.5​, −2.9​, −2.99​, and −2.999. Sketch the curve and tangent line

  48. 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.....

  49. 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

  50. math

    Consider the parabola y = 6x − x2. (a) Find the slope of the tangent line to the parabola at the point (1, 5)

  51. Calculus

    At what point does the normal to y=-5-1x+3x^2 at (1, -3 ) intersect the parabola a second time? Answer: Note: You should enter a cartesian coordinate. The normal line is perpendicular to the tangent line. If two lines are perpendicular their slopes are

  52. 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

  53. 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

  54. 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

  55. Calculus

    Sketch a graph of the parabola y=x^2+3. On the same graph, plot the point (0,−6). Note there are two tangent lines of y=x2+3 that pass through the point (0,−6). The tangent line of the parabola y=x^2+3 at the point (a,a^2+3) passes through the point

  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

    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

  58. maths geometry

    Find and write down a proof that the product of the gradients of two perpendicular lines is -1 Use trigonometry. Let the slope of a line from A to B be m1. Let the slope of a perpendicular line from A to C be m2. The tangent (or slope) of the line between

  59. calculus

    First I would find the first derivative which is the slope and then would I plug in the given value into the original equation to find y and then use y-y_1=m(x-x_1)? Find the euation of the tangent line at the given value a) y=ln abs(x+4) x = -3 b) y= (x^2

  60. 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))

  61. math

    Consider the parabola y = 7x - x2. (a) Find the slope of the tangent line to the parabola at the point (1, 6). 1

  62. Math

    If f(x)=3x^2-5x, find the f'(2) & use it to find an equation of tangent line to the parabola y=3x^2-5x at the point (2,2). My ans is f'(2)=7 & y=7x-12. What is parabola exactly? & is the any possibility if the eqtn of f(x) is not the same with parabola

  63. cal

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph the quadratic

  64. calculus I

    Problem: Consider (1) the parabola y=3-1/10 x^2 and (2) the upper half of the circle centered at (20, 0) with radius of 10. Find the points on the parabola where the tangent line is also tangent to the upper half of the circle. (You can find these points

  65. 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.

  66. math

    Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x)=-10/3x^2+6x+6; (-1, -10/3) slope ?? tangent line y = ?

  67. Math Please Help!!

    Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x)=-10/3x^2+6x+6; (-1, -10/3) slope ?? tangent line y = ?

  68. calculous

    Find the area of the region bounded by the parabola y = 4x^2, the tangent line to this parabola at (4, 64), and the x-axis.

  69. 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.

  70. Math

    Let f(x) be the parabola -x^2+16x-16. find the point (x,y) on f such that tangent line to f at (x,y) passes through the origin. My ans is (8,48). First i do f'x then i find x and lastly i find y. I do this because the max/min point is the point where

  71. calculus

    Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line.f(x)= x^2 - 5x +2 (1, -2)

  72. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 7 x - 2 x^2 text( at ) \(-1,-9\) m = y =

  73. Calculus

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 15/(4 x) at (1,(15/4) m = y =

  74. Calculus

    Find the slope of the tangent line to the curve y = (x^2 -8)^6 at x = 3, and write the equation of the tangent line.

  75. 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

  76. calculus

    I'm feeling pretty stupid right now because I can't remember how to do these. if f(x) = (2x-5)/(x^2-4), write an equation of the tangent line to f at point x=0. *How do I find the slope of the tangent line? and how do you put x=ln4 into a y= equation? Take

  77. 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

  78. Math -Precal 11

    Show that the point P(7,7) is on the perpendicular bisector of the line segment joining A (6,-1) to B (0, 3). Also, verify that P is the same distance from A and B. For what values of k is the line y=l tangent to the circle (x-3)^2 + (y+2)^2 = 36? Thanks!

  79. Math

    I have a series of questions that I did. They lead up to the last question I can't solve. Could you check my math and help me with the last question? Thanks! a) Let a be the point (2,3). Compute the distance from Origin 0 to A answer: a^2 + b^2 = c^2 3^2 +

  80. Pre-Calculus

    Im having trouble with this. Find an equation of the tangent line to the parabola at the given point and find the x-intercept of the line. x^2=2y (4,8)

  81. Calculus 1

    Find the slope of the tangent line and the equation of the tangent line to f(x)=x^2-x at x=3

  82. 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

  83. 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.

  84. calculus

    find the parametric equation of the line that is tangent to the parabola y=x^2 at the point(-2 , 4)

  85. Calculus

    find the slope of the tangent line to the parabola y=x^2+3x at the point (-1, -2) using lim x-->a (f(x)-f(a))/x-a

  86. maths

    consider the line y=6x-k and the parabola y=x^2 i) for what value of k is the line y=6x-k a tangent to the parabola y=x^2 ? ii) the line y=6x-k intersects the parabola in two distinct places. what is the largest integer value that k can take ?

  87. Calculus

    Find the slope and the equation of the tangent line to the graph of the function f at the specified point. f(x) = -8/5 x^2 + 7 x + 7;(-1, -8/5) slope tangent line y =

  88. 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

  89. 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

  90. Applied Calculus......

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=6x-5x^2 at (-2, -32) I have to use the four step process, but seem to be getting stuck...

  91. Calculus

    Use the four-step process to find the slope of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = -2x2-2x+1 (-1, -2)

  92. Calculus PLEASE HELP

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x) = 2 x - 4 x^2( at ) (-2,-20) m= y=

  93. 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

  94. 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

  95. Calculus

    Find all values for c in the intercal (1,4) so that the slope of the tangent line at (c,f(c)) equals the slope of the secant line through (1,1/3) and (4,2/3) where f(x) = x/(x+2) 1

  96. Pre-Cal

    Find an equation of the tangent line to the parabola at the given point, and find the x-intercept of the line. 17) x^2=2y , (-3,9/2) 18) y=-2x^2 , (-1,-2)

  97. 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

  98. math

    Find the values of a,b, and c if the parabola y=a(x^2)+bx+c is tangent to the line y=-2x+3 at (2,-1) and has a critical point when x=3

  99. Math

    find f'(x) find the slope of the graph of f a x=2 and x=4 find the equations of the tangent lines at x=2 and x=4 and find the value(s) of x where the tangent line is horizontal. f(x)=2x^2+8x I found that f'(x)=4x+8 and that the slopes were 16 and 24 and

  100. Calculus 1

    I know it's hard to draw a graph here, but I just need an explanation of both if possible. I appreciate any help I can get! :) "Determine whether the following statements are true and give an explanation or counterexample. Explain why or why not, using

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