Results 1 to 3 of 3

Thread: One more Calculus Problem

  1. #1
    Newbie
    Joined
    Nov 2007
    Posts
    16

    One more Calculus Problem

    4. Let f(x) and g(x) be the differentiable functions graphed here. At x=c, the vertical distance between these curves is the greatest. Is there anything special about the tangents to the two curves at x=c? Give reasons for your answers. f(x) is the line that is concave up, and g(x) is the line that is concave down.

    I am in the first semester of calculus, so this would have to apply to that.... but I have no clue where to start on this one :P. So help would be nice.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Nov 2007
    Posts
    16
    Forgot to put the graph here.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    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 Prophet View Post
    4. Let f(x) and g(x) be the differentiable functions graphed here. At x=c, the vertical distance between these curves is the greatest. Is there anything special about the tangents to the two curves at x=c? Give reasons for your answers. f(x) is the line that is concave up, and g(x) is the line that is concave down.

    I am in the first semester of calculus, so this would have to apply to that.... but I have no clue where to start on this one :P. So help would be nice.
    the vertical distance between the functions at any value of $\displaystyle x$ is given by $\displaystyle f(x) - g(x)$. define a new function, $\displaystyle h(x)$, to be this distance. thus we have:

    $\displaystyle h(x) = f(x) - g(x)$

    now we want to maximize $\displaystyle h$. so we find its derivative and set it equal to zero, thus we have:

    $\displaystyle h'(x) = f'(x) - g'(x) = 0$

    what can we say about $\displaystyle f'(x)$ and $\displaystyle g'(x)$? which are the slopes of the tangent lines of $\displaystyle f(x)$ and $\displaystyle g(x)$ respectively
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with calculus problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 25th 2010, 11:05 AM
  2. Replies: 1
    Last Post: Jun 7th 2008, 11:47 AM
  3. Help with this Calculus Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 30th 2006, 06:03 PM
  4. Calculus Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Mar 19th 2006, 10:24 AM
  5. Calculus Problem!!!!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 18th 2006, 10:10 PM

Search Tags


/mathhelpforum @mathhelpforum