Results 1 to 4 of 4

Math Help - Finding tangent to function parallell with line

  1. #1
    Newbie Bato91's Avatar
    Joined
    Dec 2009
    From
    Gothenburg
    Posts
    5

    Finding tangent to function parallell with line

    Hello all! I just found this forum and registered. I would like some help with the following problem:

    What is the function of the tangent to the parable y=x^2 , parallell with the line  y=6x ? I can see where the tangent is graphically and go from there, but how can you solve it solely by equating?


    (feel free not to copy my terminology; I'm not good at English and may use some odd names)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Nov 2009
    Posts
    277
    Thanks
    2

    Derivative

    Your function
    <br />
y = 6 x<br />

    has slope 6.

    Your function
    <br />
y = x ^ 2<br />

    has derivative:
    <br />
\frac { d y } { dx } = 2 x<br />

    which has slope 6 at x=3. Thus y = 9. The tangent line must be y=6x-9.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie Bato91's Avatar
    Joined
    Dec 2009
    From
    Gothenburg
    Posts
    5
    Thank you!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,807
    Thanks
    116
    Quote Originally Posted by Bato91 View Post
    Hello all! I just found this forum and registered. I would like some help with the following problem:

    What is the function of the tangent to the parable y=x^2 , parallell with the line  y=6x ? I can see where the tangent is graphically and go from there, but how can you solve it solely by equating?


    (feel free not to copy my terminology; I'm not good at English and may use some odd names)
    Here is a different approach:

    The tangent line has the equation: t: y = 6x + b

    Now calculate the coordinates of the intersection between the parabola and the straight line:

    x^2=6x+b~\implies~x^2-6x-b=0

    Use the formula to solve this quadratic equation:

    x = 3\pm\sqrt{9+b}

    You get only one intersection point (=tangent point) if the radicand equals zero:

    9+b = 0~\implies~\boxed{b=-9} . Consequently the tangentpoint is T(3, 9)

    Therefore the equation of the tangent line becomes: t: y = 6x-9
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 6
    Last Post: January 12th 2011, 02:38 PM
  2. Replies: 7
    Last Post: December 5th 2009, 08:53 AM
  3. Finding tangent line of a function
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 11th 2009, 10:10 AM
  4. finding a tangent line.......
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 9th 2009, 03:39 PM
  5. Finding a tangent line
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: June 12th 2009, 05:14 PM

Search Tags


/mathhelpforum @mathhelpforum