APPM 2350 Final: appm2350fall2017examfinal_sol

• School: CU-Boulder
• Department: Applied Math
• Course: APPM 2350
• Professor: All

Document Summary

Fall 2017: (30 points) determine the absolute maximum and minimum values of the function f (x, y) = 20 16x 4y + 4x2 + Be sure to clearly give both the locations and values of the absolute extremum. y3. The given function is a polynomial and therefore its domain is all of r2, which is unbounded. Thus the function need not y3 attain a maximum nor a minimum. Consider the trace for a xed x = x0. 3 (cid:21) = lim: 4y + As an aside, the function may possess local maxima or minima and/or saddle points. Indeed, given f (x, y) = 20 16x . , take the rst partial derivatives, set them equal to zero and solve the resulting system of equations. y3. 3 fx(x, y) = 16 + 8x = 0 fy(x, y) = 4 + y2 = 0. Critical points are thus (2, 2) and (2, 2).