Math

posted by .

1. The curve y=10/2x+1 -2 intersects the x-axis at A. The tangent to the curve at A intersects the y-axis at C.
(i) Show that the equation of AC is 5y+4x=8
(ii) Find the distance of AC

2. The equation of a curve is y=1/6(2x-3)^3-4x
(i) Find dy/dx
(ii) Find the equation of the tangent to the curve at the point where the curve intersects the y-axis.

  • Math -

    the curve intersects the x-axis at (2,0)
    y'(x) = -20/(2x+1)^2
    y'(2) = -4/5

    tangent at (2,0) is
    y = -4/5 (x-2)
    intersects the y-axis at (0,8/5)

    AC is thus
    y = (x-2)(-4/5)
    5y = 8-4x
    5y+4x=8

    -------------------------------

    y = 1/6 (2x-3)^3 - 4x
    y' = (2x-3)^2 - 4

    the curve has y-intercept at (0,-9/2)

    y'(0) = 5
    so, the line is

    y+9/2 = 5x

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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 …
  2. trig

    The parametric equations for a curve in the x-y plane are x=2+t^2 and y=4-3t. Determine the points where the curve intersects the x-axis.
  3. maths

    2. The tangent to the curve y = ex2 drawn at the point (e, ee) intersects the line joining the points (e - 1, ee-1) and (e+1, ee+1) 3. A hyperbola, having the transverse axis of length 4 sin, is confocal with the ellipse 3x2 + 4y2 …
  4. maths

    Find the equation of the curve through (4,2) whose tangent (for x > 0) forms an angle with the x-axis, the tangent of which is equal to 1 . Sketch the curve for x x > 0. √
  5. Calculus

    The graph of the equation x2 − xy + y2 = 9 is an ellipse. Find the lines tangent to this curve at the two points where it intersects the x-axis. Show that these lines are parallel.
  6. Math

    Suppose p and q are points on the unit circle such that the line through p and q intersects the real axis. Show if z is the point where this line intersects the real axis, then z=(p+q)/(pq+1) So far I've figured out that the equation …
  7. 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?
  8. Calculas-Differentiation

    Find the equation of the tangent to the curve y=1/2x^2-4x-3at the point where the curve intersects the y-axis.
  9. calculus

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

    1. Given the following polynomial: 2x^2 + 7x - 15 = 0 Check all that apply.  The value of the discriminant is 169.  There are 2 real roots.  There are 2 irrational roots.  The graph intersects the y-axis twice.  The …

More Similar Questions