Find the function f, given that the slope of the tangent line at any point (x,f(x)) is f '(x) and that the graph of f passes through the given point. f '(x)=6(2x-7)^5 at (4, 3/2)

134,312 results
  1. calculus

    5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the secant line on the interval [1,

  2. 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 =

  3. 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

  4. 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 = ?? .

  5. I would like to understand my calc homework:/

    Consider the differential equation given by dy/dx=(xy)/(2) A) sketch a slope field (I already did this) B) let f be the function that satisfies the given fifferential equation for the tangent line to the curve y=f(x) through the point (1,1). Then use your

  6. 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

  7. 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

  8. 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

  9. Math

    Find the function f, given that the slope of the tangent line at any point (x,f(x)) is f '(x) and that the graph of f passes through the given point. f '(x)=6(2x-7)^5 at (4, 3/2)

  10. Calculus

    1. a) For the Function and point below , Find f’(a). b) Determine the equation of the line tangent to the graph of f at (a,f(a)) for the given value of f(x) = 4x2+2x, a =1 F’(a) = y = 2. For the function find f’ using the definition f’(x) =

  11. 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

  12. 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

  13. MATH

    Find the slope of the tangent line to the graph of the function at the given point. g(x) = 7/2x + 9, (-2, 2)

  14. 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

  15. 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

  16. 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

  17. Calculus

    The figure below shows a function g(x) and its tangent line at the point B=(2,6.8). If the point A on the tangent line is (1.94,6.87), fill in the blanks below to complete the statements about the function g at the point B. g(2)= _____ g(2)= _____ I found

  18. 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 =

  19. calculus

    f(x)=3-5x , (-1,8) find the slope of the tangent line to the graph of the function at the given point how do you figure this out?

  20. cal

    Equations of the tangent lines to hyperbola xy=1 that pass through point (-1,1) I know the graph of y=1/x but not sure about the tangent lines at given point. Are the lines tangent to (1,1) and (-1,-1)? You're correct, the graph is y=1/x, so find y' to get

  21. 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

  22. 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

  23. math

    Find the slope m and an equation of the tangent line to the graph of the function f at the specified point. f(x)=x^2/x+4 ;(1,1/5) m =?? y =??

  24. Calc problem

    Consider the function y=(kx)/(x-k) a. Show that y is symmetric with respect to the line y=x. b. Write the equations of the horizontal and vertical asymptotes of y. c. Find the point(s) of intersection of y with the line x-y=-2k, and find the slope of the

  25. Calculus

    Let (a, b) be any point on the graph of Prove that the area of the triangle formed by the tangent through (a, b) and the coordinate axes is 2. This is the solution from the solution manual The coordinates of the point are (a,1/a). The slope of the tangent

  26. 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

  27. 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)

  28. 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...

  29. 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

  30. 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

  31. got a couple of calculus questions

    1. What is the equation of the tangent line to y = 2*x(x - 4)^6 at point (5, 10)? 2. If f(x)=8/(x^2+4) , find the slope of the curve at the point (2, 1). 3. The demand function for an item is given by x=200[1-(p/(p+2))] . At what rate is the demand

  32. Calculus Please someone help

    1. Find the slope m and an equation of the tangent line to the graph of the function f a the point (2, 38) 2. Find an equation of the line that passes through the point (9,7) and is perpendicular to the line 5x+3y-4=0

  33. 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

  34. 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!

  35. calculus

    Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.) f(x) = 2x^2 + 7x

  36. calculus

    find a function f given that (1) the slope of the tangent line to graph of f at any point P(x,y) is given by dy/dx=3xy and (2) the graph of f passes through the point (0,2)

  37. 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

  38. 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.

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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 =

  44. 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 = ?

  45. 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 = ?

  46. College Math

    2008 (2nd)Course2-4.1 We are to find a function f(x) such that its derivative is x^2+x-1 and the graph of y=f(x) is tangent to the straight line y=x+1. First we find the coordinates of the point at which y=f(x) and y=x+1 are tangent.Since the slope of the

  47. 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)

  48. 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 =

  49. Math

    1. The slope of the tangent line to a function at a point is equivalent to __. a. the slope of the secant at that point b. the slope of the cosecant at that point c. the rate of change of the function at that point d. the slope of the secant near that

  50. 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=

  51. 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=

  52. 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)

  53. 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 =

  54. 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.

  55. 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

  56. 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

  57. 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

  58. 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

  59. 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)

  60. MATH

    Find the slope of the tangent line to the graph of the function at the given point. g(x) = 7/2x + 9, (-2, 2)

  61. MATH

    Find the slope of the tangent line to the graph of the function at the given point. g(x) = 17 − x^2; (3, 8)

  62. calculus

    Find the slope of the tangent line to the graph of the function at the given point. g(x) = 3 x + 4, (-4, 1)

  63. calculus

    f(x)=3-5x , (-1,8) find the slope of the tangent line to the graph of the function at the given point

  64. math

    Find the slope m and an equation of the tangent line to the graph of the function f at the specified point. f(x)=x^2/x+4 ;(1,1/5) m =?? y =??

  65. Calculus A

    1. Find the slope m and an equation of the tangent line to the graph of the function f a the point (2, 38) f(x)=9x -2x +6

  66. Calculus

    1. Find the slope m and an equation of the tangent line to the graph of the function f a the point (2, 38) f(x)=9x -2x +6

  67. math

    Find the slope m and an equation of the tangent line to the graph of the function f at the specified point. f(x)=x^2/x+4 ; (3,9/7)

  68. math

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

  69. 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

  70. Calculus

    The equation dy/dx = -6x^2/y gives the slope at any point on the graph of f(x). The range of f(x) is [0, infinity] and f(1) = 2. A. Find the equation of the tangent line to f(x) at the point (1,2). B. Write the function f(x). C. Determine the domain of the

  71. calculus

    Consider the following. y = x2 − 9x x2 + 5x at (3, − 3 4 ) (a) At the indicated point, find the slope of the tangent line. (b) At the indicated point, find the instantaneous rate of change of the function.

  72. calculus

    Find a function f(x) = a + b sqrt(x) that is tangent to the line 2y - 3x = 5 at the point (1,4) AND Find a function of the form f(x)=c+dcoskx that is tangent to the line y=1 at the point (0,1) and tangent to the line y=x+(3/2) - (pi/4) at the point

  73. 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

  74. Calculus

    So here is the question: Find and equation of the tangent line to the graph: 4)f(x)=e^(2x) passing through the point (0,0) I find derivative being f'(x) =2e^(2x) Then m = f'(0) = 2 put into point slope formula: (y-y1)=m(x-x1) y-0 = 2(x-0) which comes out

  75. 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 +

  76. 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

  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. Calculus derivative

    find the slope m and an equation of the tangent line to the graph of the function f at the specified point. original: x^2/x+10 point: (3,9/13) After I found the derivative: (x+10)(2x)-(x^2)(1)/((x+10))^2 How do I get the slope? Should I put 3 into the

  79. calculus

    Consider the following. y = (2x2 + 5)(x3 − 25x) at (5, 0) (a) At the indicated point, find the slope of the tangent line. (b) Find the instantaneous rate of change of the function.

  80. 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

  81. 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

  82. 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

  83. calculus

    This is from our problem set. f(x)= 2(x^3)-3(x^2)-12x+20 write an equation of the line perpendicular to the graph of f at x=0 I think i'm supposed to take the derivate of f and then find the slope of the tangent line at x=0. Then take the opposite

  84. 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))

  85. 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

  86. 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

  87. 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

  88. 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

  89. 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

  90. Calculus

    Would you be able to help me with a couple of questions? thanks in advanced! 1. I am given the graph f(x)=x^2-2x. I have to draw a line tangent to the point (0,0). Then, I have to estimate the slope at that point. how would I go about answering this

  91. Calculus Need of Urgent help

    find the indicated limits, if they exist. 1. lim (3x^3+x^2+1)/(x^3+1) x-> -infinity 2. find the slope of the tangent line to the graph of the given function at any point: f(x) = 2x +7 Could anyone please, please, please explain to me how to do these

  92. calculus

    what is the slope of the tangent line passing through the point (2,3) of the graph of this function? f(x)=x^2+2x-5 A 1 B 2 C 3 D 4 E 6

  93. Math - PreCalc (12th Grade)

    What is the slope of the tangent line passing through the point (2, 3) of the graph of this function? f(x)=x^2+2x−5 A) 1 B) 2 C) 3 D) 4 E) 6 f(2)=2^2+2(2)-5 f(2)=3 so is it c?

  94. 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.....

  95. Algebra

    Given a line containing the points(1,4), (2,7) and (3,10) determine that slope-intercept form of the equation, provide one additional point on this line, and graph the funtion. Start by putting the first point into point-slope form: y-y1=m(x-x1), so

  96. 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

  97. Calculus

    Given x^2+y^2=4, find the equation of the tangent line at the point (-1,sq.rt.3). Then, at what point is the slope 0? What point is the slope -1? I have no clue what to do!

  98. math

    i have more than one question so if u no any of the answers please tell me 1.) write the point-slope form of the equation of the line with slope -2 passing through the point ( -5, -9). 2.) write the point-slope form of an equation of the line through the

  99. Calculus

    1. a) For the Function and point below , Find f’(a). b) Determine the equation of the line tangent to the graph of f at (a,f(a)) for the given value of f(x) = 4x2+2x, a =1 F’(a) = y = 2. For the function find f’ using the definition f’(x) =

  100. Math (Calculus 121)

    Consider the following function. f(x) = 7x3 + x2 - 0.08x + 12 Find the two points on the graph at which the tangent line is horizontal. Give your values correct to 2 decimal places. ( , ) (point with smaller x value) ( , ) (point with larger x value)

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