MAT-2130 Midterm: MATH 2130 App State Fall2005 Exam2 formA
Document Summary
Integrate each component with respect to the proper variable (i goes with x, j goes with y, and k goes with z). Z 2x + yz dx = x2 + xyz + g1(y, z) Z z cos(y) + xz dy = z sin(y) + xyz + g2(x, z) Z sin(y) + xy 3z2 dz = z sin(y) + xyz z3 + g3(x, y) Putting this together we see that f (x, y, z) = x2 + xyz + z sin(y) z3 (plus an arbitrary constant c). (10 points): let f (x, y) = x2 + 2y2 + xy2 + 1. Find all critical points, then determine whether each critical point is a minimum, a maximum, a saddle point, or a nothing. The rst partials: fx = 2x + y2, fy = 4y + 2xy. We must solve the system of equations: fx = 0 and fy = 0 to nd the critical points.
