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I have how defect density in a crystal change over time. 6 data points

I want to regress this with a 4th order polynomial. I can do this and obtain 95% non-simultaneous, functional prediction intervals.

However I want the derivative function of this density ultimately, with error. Can I simply take the derivative of the upper, bottom, and lower bounds separately and call it a day? Would these derivatives mean the same kind of 95% confidence intervals for the derivative function?

Frankfurt
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    Is a confidence interval a continuous function? What variables is it a function of? – abalter Aug 28 '20 at 05:47
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    Hi. Could you add 2-3 formulas to your question? That will make it clearer to this forum. Thx. – Match Maker EE Aug 28 '20 at 06:51
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    @abalter By definition, the confidence interval is a function of the data. Whether it's a continuous one depends on the procedure used to obtain the CI. – whuber Aug 28 '20 at 14:04
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    Briefly, no: differentiating the bounds has no clear meaning and is unlikely to produce what you want. Your question can be addressed by adapting the technique for estimating derivatives in a quadratic regression at https://stats.stackexchange.com/questions/370178 and https://stats.stackexchange.com/questions/216189. – whuber Aug 28 '20 at 14:07

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