Results 1 to 7 of 7

Math Help - point of intersection

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    34

    point of intersection

    Consider the function f(x) = -2 x^2 + 9 x + 11

    (a) find [f(x+h) - f(x)]/h in the form __x+ __h+___
    (I found -4x-2h+9, which was correct)
    (b) Using the result of (a), find the derivative of f at x.
    (I found -4x+9, also correct)



    ***(c) Find the point of intersection of the two tangent lines to the parabola y = -2x^2 + 9x + 11 at the points (3,20) and (-4,-57)

    How do i do this? What are the two tangent lines they are talking about?
    I don't know where to start on this bad boy, thanks so much
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    note that (3,20) and (-4,-57) are both on the curve y = -2x^2 + 9x + 11

    find the tangent line equation to the curve at each point, then set them equal to find where they intersect.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2009
    From
    Scotland
    Posts
    41
    To find the tangent to a line you need to find the gradient of the tangent which is done by first differentiating the equation of the parabola:

     y = -2x^2 + 9x + 11
     \frac{dy}{dx} = -4x + 9
    To find the gradient at that point you need to put in the value of the x co-ordinate at the point of the tangent. In this case one of the values would be x = 3
     m = - 4*3 + 9
     m = -3

    Finally to find the equation of the tangent you now use the co-ordinates and the gradient you have just found and substitute those into the equation of a line:
     y - b = m(x - a)
     y - 20 = -3(x - 3)
     y = -3x + 29

    This is the equation of the tangent at (3,20). To find the tangent at (-4, -57) you need to repeat this process using (-4,-57) instead of (3,20).

    Arrange the equation of the second to equal y. You can then say both y values are the same so equate both tangents and solve to find the x value. Finally put this x value into either of the equations for the tangents and you will have the y value. This is your point of intersection.

    I'll give you the chance to work out the second tangent yourself by following the same process I used. If you need me to explain further just ask.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2008
    Posts
    34
    how do you differentiate y= -2x^(2) + 9x+11?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2009
    From
    Scotland
    Posts
    41
    I've done it above. See the part

    Quote Originally Posted by Amanda H View Post
     \frac{dy}{dx} = -4x + 9
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,623
    Thanks
    428
    Quote Originally Posted by williamb View Post
    Consider the function f(x) = -2 x^2 + 9 x + 11

    (a) find [f(x+h) - f(x)]/h in the form __x+ __h+___
    (I found -4x-2h+9, which was correct)
    (b) Using the result of (a), find the derivative of f at x.
    (I found -4x+9, also correct)
    you already found the derivative, or didn't you notice?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Oct 2008
    Posts
    34
    i have the point -1/2 ,30.5
    which is correct

    thank you both so much =]
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. point of intersection
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 19th 2010, 07:31 AM
  2. Point of intersection
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 19th 2010, 08:57 AM
  3. point of intersection
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: December 8th 2008, 07:37 PM
  4. Point of intersection
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 23rd 2008, 03:06 PM
  5. Point of intersection
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 10th 2008, 08:21 PM

Search Tags


/mathhelpforum @mathhelpforum