Results 1 to 6 of 6

Thread: Finding the equation

  1. #1
    Member Awsom Guy's Avatar
    Joined
    Jun 2009
    From
    Mars
    Posts
    186

    Finding the equation

    How do I find the equation of the tangent to the graph of f(x)=Sqrt x at the point x=9.
    I know the gradient of the tangent which is 1/6.
    But I have no idea how to do this.
    Any help will be appreciated.
    THANKS
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Thanks
    1
    Quote Originally Posted by Awsom Guy View Post
    How do I find the equation of the tangent to the graph of f(x)=Sqrt x at the point x=9.
    I know the gradient of the tangent which is 1/6.
    But I have no idea how to do this.
    Any help will be appreciated.
    THANKS
    f(x)=\sqrt{x} .. this is the equation of the curve .

    f(9)=3

    so y=3
    Last edited by mathaddict; Oct 21st 2009 at 07:01 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Awsom Guy
    Quote Originally Posted by Awsom Guy View Post
    How do I find the equation of the tangent to the graph of f(x)=Sqrt x at the point x=9.
    I know the gradient of the tangent which is 1/6.
    But I have no idea how to do this.
    Any help will be appreciated.
    THANKS
    As you say, f'(9) = \frac{1}{2\sqrt9}=\frac16.

    You now need f(9) = \sqrt9 = 3

    So the tangent is at the point (9,3).

    Now use y - y_1 = m(x-x_1), the equation of the line with gradient m through the point (x_1,y_1).

    When simplified, this comes to 6y = x+9.

    Can you fill in the details?

    Grandad
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2009
    Posts
    12
    i dont understand how you got 1/6 for m
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello sjara
    Quote Originally Posted by sjara View Post
    i dont understand how you got 1/6 for m
    The value of m is the gradient of the curve at the point where x = 9. We get this by differentiating f(x), and then plugging in that value, x = 6.

    f(x) = \sqrt{x}=x^{\frac12}

    \Rightarrow f'(x)=\tfrac12x^{-\frac12}=\frac{1}{2\sqrt{x}}

    So when x = 9, f'(9)= \frac{1}{2\sqrt{9}}=\frac16

    And this is the value of m, the gradient of the tangent when x = 9.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member Awsom Guy's Avatar
    Joined
    Jun 2009
    From
    Mars
    Posts
    186

    Thanks

    Thanks I managed to get that myself anyway. Thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 10
    Last Post: Dec 8th 2011, 10:27 AM
  2. Help for finding the equation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jul 20th 2009, 01:11 AM
  3. Finding Equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Nov 15th 2008, 01:20 AM
  4. Finding the new equation
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Apr 29th 2008, 04:47 PM
  5. finding the equation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Sep 16th 2007, 11:10 AM

Search Tags


/mathhelpforum @mathhelpforum