1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about finding a tangent

  1. Feb 23, 2013 #1
    1. The problem statement, all variables and given/known data

    Show that, for each real number t [itex]\in[/itex] the interval (0, 1], the curve given by:

    [itex]y=ln(\frac{x+\sqrt{1+x^{2}}}{1+\sqrt{2}})[/itex]

    has a tangent line with slope t. Find the points on the curve at which the tangent line has slope 2/3.

    3. The attempt at a solution

    I found the first derivative of this curve to be:

    [itex]dy/dx=1/\sqrt{(1+x^{2})}[/itex]

    but now not sure how to proceed.

    What do they mean when they ask me to show that for each t has a tangent line with slope t?

    any help appreciated!

    Also to find the points with dy/dx=3 I did this:

    [itex]dy/dx=1/\sqrt{(1+x^{2})} =2/3[/itex] >>>> [itex]x=\pm \sqrt{5}/2[/itex]
     
    Last edited: Feb 23, 2013
  2. jcsd
  3. Feb 23, 2013 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Do what you just did for ##t## instead of 2/3. For the points on the curve you probably want the y values too.
     
  4. Feb 23, 2013 #3
    Oh of course, lol! thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question about finding a tangent
Loading...