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Homework Help: 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:


    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:


    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


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    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
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