Results 1 to 5 of 5

Math Help - Need Help With a Tangent Line Problem

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    9

    Need Help With a Tangent Line Problem

    Could someone please help me with the following problem I'm having difficulties with.

    1) Show that the tangent line to the parabola y=Ax^2, A not equal to 0, at the point x=c will intersect the x-axis at the point (c/2, 0)

    2) Determine where this line intersects the y-axis
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by erimat89 View Post
    Could someone please help me with the following problem I'm having difficulties with.

    1) Show that the tangent line to the parabola y=Ax^2, A not equal to 0, at the point x=c will intersect the x-axis at the point (c/2, 0)

    2) Determine where this line intersects the y-axis
    First find y':

    y'=2Ax.

    Thus, the slope of the line at x=c is 2Ac.

    Thus, the tangent has the equation y-Ac^2=2Ac(x-c)\implies y=2Acx-Ac^2

    Now find where it crosses the x axis:

    0=2Acx-Ac^2\implies x=\dots.

    It crosses the y axis when x=0.

    So y=\dots

    Can you take it from here?

    --Chris
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2008
    Posts
    9

    Reply

    Maybe I'm just confused but the question wasn't asking where it intersected the x-axis the x-axis intersection is given at the point (c/2, 0) it was only asking to determine where it crossed the y-axis in part 2 of the question. Why is this point (c/2, 0) given?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Santa Cruz, CA
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by erimat89 View Post
    Could someone please help me with the following problem I'm having difficulties with.

    1) Show that the tangent line to the parabola y=Ax^2, A not equal to 0, at the point x=c will intersect the x-axis at the point (c/2, 0)

    2) Determine where this line intersects the y-axis
    Quote Originally Posted by erimat89 View Post
    Maybe I'm just confused but the question wasn't asking where it intersected the x-axis the x-axis intersection is given at the point (c/2, 0) it was only asking to determine where it crossed the y-axis in part 2 of the question. Why is this point (c/2, 0) given?
    It asks you to show that the line intersects the x-axis at the point (c/2,0).

    Since I got the equation of the line to be y=2Acx-Ac^2, at y=0, the line crosses the x-axis.

    Thus 0=2Acx-Ac^2\implies 2Acx=Ac^2\implies x=\frac{Ac^2}{2Ac}\implies x=\frac{c}{2}. So we see that it crosses the x-axis at \left(\tfrac{1}{2}c,0\right)

    \mathbb{Q.E.D.}

    Now, it intersects the y axis when x=0. Thus, we see that y=2Ac(0)-Ac^2\implies y=-Ac^2.

    Thus, the y intercept is \left(0,-Ac^2\right).

    Does this make sense?

    --Chris
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2008
    Posts
    9

    Thanks

    Makes alot of sense you clarified things for me. I've never been good with any sort of math problem that involves words for some reason I get thrown off.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. I need some help with a tangent line problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 22nd 2011, 06:04 PM
  2. Tangent Line Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 6th 2009, 03:52 PM
  3. Tangent line problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 23rd 2009, 07:38 PM
  4. Tangent line problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 7th 2008, 10:33 AM
  5. Tangent Line Problem--Please Help
    Posted in the Calculus Forum
    Replies: 5
    Last Post: November 11th 2007, 02:54 PM

Search Tags


/mathhelpforum @mathhelpforum