If you absolutely have to make sure your constraints are met, you have to change your fitting equation so that all possible solutions satisfy your constraints. Consider the 2nd degree polynomial:
if the constraints are y'(1) = 0, and y(1) = 1; we get
Your fitting equation then becomes
Which will give shitty results since it only has one degree of freedom. But this is just an example, if you start with a 4th degree polynomial, your fitting equation will have three degrees of freedom. The fit function will then take care of the rest and minimize the least squares cost.