Results 1 to 2 of 2

Thread: Horizontal Tangent Lines

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    26

    Horizontal Tangent Lines

    f(x)= xe^(x)/(9x+b)


    How would you find the coordinates of f where the tangent lines are horizonal when b=-7?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    12,880
    Thanks
    1946
    Quote Originally Posted by ctran View Post
    f(x)= xe^(x)/(9x+b)


    How would you find the coordinates of f where the tangent lines are horizonal when b=-7?
    If $\displaystyle b = -7$, then

    $\displaystyle f(x) = \frac{xe^x}{9x - 7}$.


    Tangent lines are horizontal when the derivative is $\displaystyle 0$.


    So $\displaystyle f'(x) = \frac{(9x - 7)\,\frac{d}{dx}(xe^x) - xe^x\,\frac{d}{dx}(9x - 7)}{(9x - 7)^2}$

    $\displaystyle = \frac{(9x - 7)(xe^x + e^x) - 9xe^x}{(9x - 7)^2}$


    Now let $\displaystyle f'(x) = 0$ and solve for $\displaystyle x$.


    $\displaystyle \frac{(9x - 7)(xe^x + e^x) - 9xe^x}{(9x - 7)^2} = 0$

    $\displaystyle e^x(9x - 7)(x + 1) - 9xe^x = 0$

    $\displaystyle e^x[(9x - 7)(x + 1) - 9x] = 0$


    Since $\displaystyle e^x \neq 0$ for any $\displaystyle x$, we have

    $\displaystyle (9x - 7)(x + 1) - 9x = 0$

    $\displaystyle 9x^2 +9x - 7x - 7 - 9x = 0$

    $\displaystyle 9x^2 - 7x - 7 = 0$

    $\displaystyle x = \frac{7 \pm \sqrt{301}}{18}$.


    Now, substitute these values of $\displaystyle x$ back into $\displaystyle f(x)$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding horizontal tangent lines
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 15th 2009, 07:43 AM
  2. Replies: 2
    Last Post: Jun 22nd 2009, 05:51 PM
  3. Replies: 2
    Last Post: Jan 25th 2009, 08:41 PM
  4. x coordinates of horizontal tangents lines ?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 20th 2008, 11:51 AM
  5. Horizontal and Vertical Tangent Lines
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Sep 29th 2007, 03:28 PM

Search Tags


/mathhelpforum @mathhelpforum