if you have 2 equations and 4 constants, certainly you'll find more than 1 solution.
how did you get to that answer?
edit:I notice now about the 'turning' point. I dont know if s some mathematical term in English that provides more info.
it means I dont know what turning means
if its something like , you get an extra euqation. its still not enough to provide only one solution.
but if it means that and (this is only an example, as I said I dont know what it means) you get for equations and 4 constants you can have a system and solve it for only one solution.
if it doesnt mean nothing you still have a system but you'll get more than 1 solution.
considering that, and only that, your solution is incomplete. that is only one solution, you have to find all.
with the f(x)' info you get 3 equations
you need to solve those 3. you will get something like
this means, you can choose any value for a, and calculate the values of b,c and d, with that a and get different solutions.