Results 1 to 8 of 8

Math Help - equation of normal line

  1. #1
    Member
    Joined
    Nov 2006
    From
    chicago
    Posts
    156

    equation of normal line

    A normal line to the graph of a function f at the point (x,f(x)) is defined to be the line perpendicular to the tangent line at that point. The equation of the normal line to the curve y = 3rdroot(x^2-1) at the point where x = 3 is?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,211
    Thanks
    419
    Awards
    1
    Quote Originally Posted by Mr_Green View Post
    A normal line to the graph of a function f at the point (x,f(x)) is defined to be the line perpendicular to the tangent line at that point. The equation of the normal line to the curve y = 3rdroot(x^2-1) at the point where x = 3 is?
    The tangent line has a slope equal to the derivative of the function at that point. So find the slope. Then you can get the slope of the line perpendicular to this. Now you have the slope of your normal line and you know a point that is passes through.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2006
    From
    chicago
    Posts
    156
    am i finding the derivative of 3rdroot(x^2-1) ??
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Mr_Green View Post
    am i finding the derivative of 3rdroot(x^2-1) ??
    yes, that's the function you were given correct? it's the same procedure in finding the tangent line, except you use the negative reciprocal of the slope of the tangent line
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2006
    From
    chicago
    Posts
    156
    so for the derivative i got:
    3(x^2 - 1) * 2x =

    6x(x^2 - 1)

    is this correct?

    if so, now what do i do?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,211
    Thanks
    419
    Awards
    1
    Quote Originally Posted by Mr_Green View Post
    so for the derivative i got:
    3(x^2 - 1) * 2x =

    6x(x^2 - 1)

    is this correct?

    if so, now what do i do?
    You have
    \sqrt[3]{x^2 - 1} = (x^2 - 1)^{1/3}

    The derivative of this is
    \frac{d}{dx}(x^2 - 1)^{1/3} = \frac{1}{3}(x^2 - 1)^{-2/3} \cdot 2x

    Now do the rest I told you. Find the slope for x = 3, use this to find the slope of your normal line, then use that slope and the fact that the normal line passes through the point (x, \sqrt[3]{x^2 - 1} for x = 3.

    -Dan
    Last edited by topsquark; October 4th 2007 at 05:41 AM. Reason: Ugh. Two derivatives wrong in the same day!
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Nov 2006
    From
    chicago
    Posts
    156
    im getting y +12x=38, which is also one of my multiple choice responces, so I hope its right.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,211
    Thanks
    419
    Awards
    1
    Quote Originally Posted by Mr_Green View Post
    im getting y +12x=38, which is also one of my multiple choice responces, so I hope its right.
    There are some serious problems here.

    The slope of the tangent line at x = 3 is 1/2. So the slope of the normal line is -2. You know this line passes through the point (3, 2). I get that the normal line is
    y = -2x + 8

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Equation of the normal line?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 27th 2011, 08:27 PM
  2. the equation of normal lline/tangent line
    Posted in the Calculus Forum
    Replies: 6
    Last Post: February 17th 2010, 12:47 PM
  3. equation of tangent, normal line and vertex?
    Posted in the Calculus Forum
    Replies: 8
    Last Post: February 10th 2010, 10:22 PM
  4. Equation of the normal line
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 1st 2009, 07:10 PM
  5. equation of the normal of the line on point..
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 15th 2008, 11:13 PM

Search Tags


/mathhelpforum @mathhelpforum