Which Type of Statistical Test Do I Choose From for Finding Optimum, and How Would I Calculate It?

Question

So currently I am working on a study about carrying concentrations of Aloe vera gel % and how it affects the growth density of probiotics (in OD₆₄₀ units) to find out which concentration of Aloe gel produces the optimum/highest OD₆₄₀. Therefore, in excel I chose the polynomial type trendline order 2 (y= -(ax²+bx+c)) instead of linear since I am aiming for the optimum. I have also gotten an R² value to know how accurate the data points are towards the equation. Now my question is which statistical test do I use in order to find out whether the peak of the equation (optimum) is statistically the optimum. I was only taught the Pearson's correlation test, however my biology teacher told me that it can only be applied for linear equations.

Answer 1

yes. please contact me to illustrate it for you.