Id like to draft a conclusion to a chpter in my math aper by saying that in taking the values for P_2_eta for local maxima and the endpoints of each interval of the piecewise continuous function P_2_eta, we find that it has a maximum value of 1/48 at eta=0. Now what we have to do is repeat the process in construction a piecewise continuus function for P_1_eta and find all its max values at each of its maxima and endpoints and check that the sum of P_1_eta+P_2_eta does not exceed the value of 1/48 anywhere along the interval of eta \in [0,1] nor does it equal 1/48 but for at eta=0