It's been a while since my last calc course and I'm not sure if I even encountered how to do this but is there a way to derive a function of a concave downward sloping curve given two or more points and their respective slopes? I'm obviously aware how the curve looks but I would like to know how to derive the function if at all posible. i.e. (2,10) slope -8 and (6,4) slope -1/2, this curve has a negative decreasing slope and is concave towards the (0,0) origin. The curve's appearance is obvious from the information given but is there a way to derive a general function for this curve?