We are given that N represents the nitrogen level in the soil, and we note that this must be a non-negative value, sowe need to maximize the given functionY= kN16+N2,for N0. Sowe recall the first derivative test for absolute extrema values which states that ifcis a critical number of a continuous function Y defined onan interval, then the following holds.If Y(N)>0 for all Nc, then Y(c) is the absolute maximum value ofY.If Y(N)<0 for all n0 for all N>c, then Y(c) is the absolute minimum value ofY.To apply this test we must first find Y(N). Doing so gives the following result.Y(N)= kN16+N2Y(N)= Setting this derivative equal to0 and solving for Nin the interval N0 gives the following result.N= Applying the test, we see that there isanabsolute ---Select--- at this value ofN.