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The radius of a circular disk is given as 28 cm with a maximum error in measurement of 0.2 cm. (a) Use differentials to estimate the maximum error (in cml) in the calculated area of the disk. (Round your answer to two decimal places.) x cm2 (b) What is the relative error? (Round your answer to four decimal places.) X What is the percentage error? (Round your answer to two decimal places.) | Ix % : Enteranumber. 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=, 16+N2 where k is a positive constant. What nitrogen level gives the largest yield? Step 1 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 = , 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 Ydefined on an interval, then the foil! - If Y'(N) > O for all N c, then Y(c) is the absolute maximum 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 following result. ( )_ 16+N2 Y'(N) = kl167N2)2 kl.\\'2+l(ili'2k.\\'3 (16+N2l (.\\"2+16)2 Setting this derivative equal to 0 and solving for N in the interval N 2 0 gives the following result. H, W Applying the test, we see that there is an absolute maximum .j _.2 maximum at this value of N. We have determined that for the given yield function there is an absolute maximum when N = 4. This allows us to state the nitrogen level that gives the highest yield. Submit gyou cannot come back)