1. Calc

    Line L is tangent to the graph of y= x- (x^2/500) at the point Q a) find the x coordinate of point Q B) right an equation for line L C) suppose the graph above were a hill (measured in feet). There is a 50 foot tree growing vertically at the top of the
  2. Calc

    Line L is tangent to the graph of y= x- (x^2/500) at the point Q a) find the x coordinate of point Q B) right an equation for line L C) suppose the graph above were a hill (measured in feet). There is a 50 foot tree growing vertically at the top of the
  3. Calculus

    Line l is tangent to the graph of y= x - x²/500 at point Q & it crosses the y-axis at (0, 20) a). Find the x-coordinate of point Q b. Write an equation for line l c) Suppose the graph of y=x-x^2/500, where x and y are measured in feet, represents a hill.
  4. 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
  5. 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.
  6. 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
  7. Math- calculus

    Given f(x) = x ^ 3 - x ^ 2 -4x +4 Find the zeros of f. Write an equation of the line tangent to the graph of f at x = -1 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0,-8) which is not of the
  8. Calculus

    1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. The point (a, b) is on the graph of f and the line tangent to the graph at (a, b) passes through the point
  9. AP Calculus

    Suppose that f has a continuous second derivative for all x, and that f(0)=1, f'(0)=2, and f''(0)=0. A. Does f have an inflection point at x=0? Explain your answer. B. Let g'(x) = (3x^2 + 2)f(x) + (x^3 + 2x + 5)f'(x). The point (0,5) is on the graph of g.
  10. Math--Calculus

    Let y = f(x) be the continuous function that satisfies the equation x^4 - (5x^2)(y^2) + 4y^4 = 0 and whose graph contains the points (2,1) and (2,2). Let L be the line tangent to the graph of f at x = 2. (a) Find and expression for y'. (b) Write an
  11. 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,
  12. 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
  13. 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
  14. Algebra

    graph the equation x-3=y (where do I plot the points?) find the intercepts and then graph: 5x+4y=20 find the intercepts and then graph: 1.4x-1.3y=3.64 graph the equation using slope and y-intercept: y=10/7x +4 graph using slope and y-intercept: x+2y=8
  15. 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
  16. 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
  17. 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
  18. 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
  19. Calculus

    The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals of (0.12,1), if any,
  20. Algebra

    A line intersects the graph of y= x^2 twice. One point has an x- coordinate of -4, and the other point has an x-coordinate of 2. A) Draw a sketch of both graphs, and find the equation of the line. B) Find the measure of the angle that the line makes with
  21. Algebra

    A line intersects the graph of y= x^2 twice. One point has an x- coordinate of -4, and the other point has an x-coordinate of 2. A) Draw a sketch of both graphs, and find the equation of the line. B) Find the measure of the angle that the line makes with
  22. 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
  23. Calculus

    Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why f(x) must have a root between x=-3 and x=-2 b) Write an equation of the line perpendicular to the graph of f at x=0 c) Find the x and y coordinates of the point on the graph of f where
  24. Calculus

    Given the function defined as f(x)=x^3-(3/2)x^2-6x+10 a) Explain why f(x) must have a root between x=-3 and x=-2 b) Write an equation of the line perpendicular to the graph of f at x=0 c) Find the x and y coordinates of the point on the graph of f where
  25. Calculus

    How do you find the original function given a point (a,b) and the equation of the line tangent to the graph of f(x) at (a,b). For example: The point is (4,-11) and 7x-3y=61 is the equation of the line tangent to the graph of f(x)
  26. 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
  27. Math

    A line intersects the graph of y=x^2 twice. One point has an x-coordinate of -4, and the other point has an x- coordinate of 2. A. Find the equation of the line. B. Find the measure of the angle that the line makes with the x-axis.
  28. calc

    let f be function given by f(x)= Ln(x)/x for all x> 0. the dervative of f is given by f'(x)= (1 - Ln(x))/x squared. a) write equation for the line tangent to the graph of f at x=e squared b) Find the x-coordinate of the critical point of f. Determine
  29. 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
  30. calculus

    Find the equation of the tangent line to the graph of f(x)=4ln(9x+2)at the point of x-coordinate x=2.
  31. math, a.p. calc

    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. Write an equation for the tangent line to the graph of g at the point where x = 3. Does this tangent
  32. Calculus

    Find the equation of the tangent to the graph of f(x)=2x^4 (to the power of 4) that has slope 1. Derivative is 8 x^3. This equals 1 at x = 1/2. At this point the y-coordinate is f(1/2) = 1/8. The equation of the tangent line is thus: 1/8 + 1*(x-1/2) = x -
  33. Calculus

    find an equation of the tangent line to the graph of the function f through the point (xsub0, ysub0) not on the graph. TO find the point of tangency (x,y) on the graph of f, solve the equation ....
  34. math

    This is a continuous from my last question 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. On what intervals is the graph of g concave down?
  35. 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
  36. 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
  37. calculus

    find the x coordinate of each point at which the line tangent to the graph of f(x)=x^4-3x^2 is parallel to the line y= -2x+4
  38. precalculus

    Find (a) the equation of a line that is parallel to the given line and includes the given point, and (b) the equation of a line that is perpendicular to the given line through the given point. Write both answers in slope-intercept form. (c) Graph both of
  39. 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
  40. calculus

    Help! I have a test tommorow! I don't understand (b), (c), (e), and (g). The answers are listed following the each question. Here's a discription of the graph: There is a graph of a function f consists of a semi circle (-3 to 1 faced downward on the
  41. 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
  42. calculus

    i'm not sure how to do this. can someone help, please? thanks! consider the function f(x0 = x^2 + 2x on the interval [-2, 2] a. draw a sketch of the graph of f(x). find the average rate of change on the interval [-2, 2] and sketch this secant line. b. find
  43. calc

    The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b. I have no clue how to solve
  44. calculus

    The function f is defined by f(x) = x^3 - x^2 - 4x + 4 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, -8) which is not on the graph of f. Find the values of a and b. I have no clue how to solve
  45. Calculus

    Graph the function f(x)=x+4/x Graph the secant line that passes through the points (1,5) and (8,8.5) on the same set of axes Find the number c that satisfies the conclusion of the Mean Value Theorem for f on [1,8] c= Notice that if you graph the tangent
  46. 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
  47. 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
  48. 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)
  49. Math (Slope of inverse tangent line)

    Given the graph, goo.gl/photos/VTMjKvNsVvAQwe3X6 a) What is the slope of the tangent line to the graph of f^-1 at the point (-1/2,-1)? b) What is the slope of the tangent line to the graph of f^-1 at the point (1,2)?
  50. 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
  51. math

    With regards to question J: The variables x and y are connected by the equation y = x2 - x - 5. Some corresponding values of x and y are given in the table below. x -4 -3 -2 -1 0 1 2 3 4 5 y 15 7 a -3 -5 b -3 1 7 15 (a) Calculate the values of a and b (b)
  52. Calculus

    Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the following equation of f '(x). f '(x) = y0 − y/x0 − x f(x) =
  53. 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,
  54. 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 =
  55. 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)
  56. 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)
  57. 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=
  58. 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 =
  59. 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 = ?? .
  60. 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=
  61. math graphs

    4. Which equation would you use to find out if the two lines in the graph are parallel? (1 point) LINE #1: point a: 1, 4 point b: -2, 1 LINE #2: point c: 3, 3 point d: -1, -1 a. 4 - 1/-2 - 1 = 3 - 1/3 - 1 b. 4 - 1/-2 - 1 = 3 - (-1)/3 - (-1) c. 4 - 1/1 -
  62. 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)
  63. 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...
  64. math

    y = 2.5 ·4^x as the equation for the blue line shown in the graph, rather than the equation given in your text. Note that your line will now be tangent to the graph at the point ( 0, 2.5 ). Enter the value of c here
  65. 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,
  66. 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) =
  67. 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) =
  68. Calc

    Write the equation of the line tangent to the graph of the function at the indicated point. As a check, graph both the function and the tangent line you found to see whether it looks correct. (1/x^3 -x)^2 at x= 2
  69. Math/Algebra

    Please help me with this, below is a question I have to answer…below that is my answer…did I do, or answer this correctly? Post a response of at least 50 words to the following: Explain how to graph linear equations using the x- and y-intercepts.
  70. calculus

    Find an equation of the tangent line to the graph at the given point. (The graph is called a Witch of Agnesi.) f(x)= 7 / x^2 + 3 (2,1)
  71. calculus

    Find the equation of the line tangent to the graph of the given function at the point with the indicated x-coordinate. f(x)=(4 sqrt(x)+7)/(sqrt(x)+2); text( ) x=4
  72. Math-due today, need a check

    Please help me with this, below is a question I have to answer…below that is my answer…did I do, or answer this correctly? Post a response of at least 50 words to the following: Explain how to graph linear equations using the x- and y-intercepts.
  73. Calc II

    1) Find the point on the graph of y=x^2 where the cube has slope 5/2 2) Find the point on the graph of y=x^2 where the tangent line is parallel to the line -4x+3y=3
  74. college math

    find the slope of the tangent line to the graph of f at the given point. Graph f and the tangen line. 9. f(x) = 3x +5 at (1.8) 10. f(x)=2x + 1 at (-1,3) Please, help me with this problems. thanks
  75. Algebra...

    Write the equation of a vertical line passing through the point (8,-4). Graph x=8 and see if that is what you want. I don't understand?!What do you mean? Do you know how to draw a graph? Plot X=8, y=0 x=8, y=2 x=8, y=4 and see what kind of a line you get.
  76. calculus

    let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the graph of f at the point P = (-2,8) intersects the graph of f again at the point Q. Find the coordinates of point Q. b. Find the coordinates of point R, the inflection point of the graph
  77. Math - point on the graph

    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
  78. Calculus

    If f(2)=3 and f'(2)=5, find an equation of a. The tangent line b. The normal line to the graph of y=f(x) at the point where x=2 So I plotted (2,3) and (2,5)...but that's not getting anywhere... Thanks
  79. graphing question

    Write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line i wrote the equation which i think is y=4x-5 i point the y intercept (0,-5) in the graph how do i find the other point would the 4x become 4/1 x y=4/1x-5 then move
  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

    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
  82. 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
  83. math

    Note: y^1 means the deriviative of... If f(2)=3 and y^1(2)=5 find an equation of the tangent line and the normal line to the graph of y=f(x) at the point where x=2.
  84. 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)
  85. Algebra

    Solve the conjunction -2<or=a+3<8 Here is my result :5<or = a<5 Graph y>or=2x+1 Given the pair of inequalities y>x+1 y<3/2x+3 graph their solution set Thanks Danielle For the first one, it's probably just a typo, but it should be
  86. Calculus

    Find the slope of the functions graph at a given point. Then find an equation for the line tangent to the graph there. f(x)=2*square root of x. (1,2) Could someone please help me figure this one out?
  87. 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
  88. 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
  89. 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
  90. Calculus

    Find the equation of the tangent line and the normal line to the graph of the equation at the indicated point. x^2-y^2=16, (5,3) I need to show work, so answers formatted in this manner would be most appreciated. Thanks! :) :)
  91. 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
  92. 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
  93. 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
  94. 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
  95. Math (Pre Cal)

    Hi, I am studying for a precalculus quiz and I do not understand this hw problem: "The tangent line to a circle may be defined as the point that intersects a circle in a single point... If the equation of the circle is x^2+y^2=r^2 and the equation of the
  96. 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 = ?
  97. 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 = ?
  98. 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 =
  99. calculous

    3.Given the function f defined by f(x)=2x^3-3x^2-12x+20 a.Find the zeros of f b.Write an equation of the line perpendicular to the graph of f at x = 0 c. Find the x and y coordinates of all points on the graph of f where the line tangent to the graph is
  100. 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