MA 26100 Final: Exam_2_Review.pdf
Document Summary
Extrema: a point is a critical point if fx(a, b) = 0 or fy(a, b) = 0. Solve for fx and fy and solve for zero. Second derivative test for local extrema: (cid:0) d = d(a, b) = fxx(a, b)fyy(a, b) [fxy(a, b)]2. If d > 0 and fxx(a, b) > 0 then f(a, b) = local min. If d > 0 and fxx(a, b) < 0 then f(a, b) = local max. If d < 0 then f(a, b) is not a local min or max (saddle point: d = 0 could be anything. How to test for absolute extrema: (cid:0) test each point on the boundary and compare. F (x,y,z) means the derivatives with respect to x, y, and z (cid:0) fx, fy, fz. G(x,y,z) means the derivatives with respect to x, y, and z (cid:0) gx, gy, gz.
