Monotonic trend lines

I am playing with trend lines. I am trying to fit a 6th order polynomial to a set of X,Y data points. After doing a search on here, I was able to get it working such that the spreadsheet properly provided the coefficients.

Here is my issue.

The orignal data is monotonic, ie, each Y point is greater than the precious point. The resulting polynomial data is mostly monotonic, but there are a few points that arent.

Is there anyway to influence the curve fit such that the data will always be monotonic ?

Thanks.

I guess the you could set up a set of X values of interest and create formulae using the coefficients that the solver is changing. Tis would allow you to set contraints that each point is greater than or equal to the point before. Not perfect but maybe useful if you choose enough X values.

No even-order polynomial is monotonic over its domain.

Perhaps you could use Solver to generate the coefficients to minimize squared error, use formulas to compute the derivative from the coefficients, and constrain that to be non-negative over the domain of the data being regressed. I don't think that's rigorous, but it's a start.

Not necessarily, but a better chance, I guess.

I think are not much natural data that is polynomial in nature.