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Find all functions in 1. quadrant which tangts form triangles

  1. Nov 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Find all functions for which any tangent in first quadrant "forms" a triangle with constant surface P. (You can assume that y'<0)



    2. Relevant equations



    3. The attempt at a solution
    Now, I know I should somehow get to differential equation and then solve it but, I haven't got a clue on how to start?

    Tangent is a linear function with ##k=\frac{y_2-y_1}{x_2-x_1}## and also equal to ##k=y^{'}(x)##..

    That is in fact everything I have so far. I've been staring and this problem for quite a while now. Please help.
     
  2. jcsd
  3. Nov 25, 2013 #2

    haruspex

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    Take a point on the curve, y = f(x). Where does the tangent at that point intersect the axes?
     
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