Tutorial Exercise A model used for the yield Yof an agricultural crop as a function of the nitrogen level N in the soil [measured in appropriate units) is kN Y=7, 16+N2 where k is a positive constant. What nitrogen level gives the largest yield? We are given that N represents the nitrogen level in the soil, and we note that this must be a non-negative value, so we need to maximize the given function kN Y:i 16+N2 for N 2 0. So we recall the first derivative test for absolute extrema values which states that if c is a critical number of a continuous function Y defined on an interval, then the followmg holds. - If Y'(N) > O for all N c, then Y(C) is the absolute maXimurn value of Y. . If Y'(N) 0 for all N > c, then Y(c) is the absolute minimum value of Y. To apply this test we must first find Y'(N). Doing so gives the followmg result. kN Viv: U 1.6+N2 Y'UV) : Setting this derivative equal to Ci and solving for N in the interval N 2 0 gives the following result. N = S Applying the test, we see that there is an absolute at this value of N. min Submit Eamon cannot come back) max