MAC 2313 Midterm: MAC2313 S98 Test 2

7. (3 pts) Find all critical points for the function f(x, y) minimum, a local maximum, or a saddle point 3ryy3 and classify each as a local 8. (3 pts) Use Lagrange multiplier to find the extreme value(s) of the function f(, y) 22232 subject to the constraint 2x-3y-4z 49

4. (3 pts) For f(x, y, z) = In(x2 + y2 + ~2), calculate frys. er' 5, (3 pts) Determine the second-order Taylor formula for the function f(z,y) = (0,0) at the point 6. (3 pts) Find all critical points for the function f(x,y) = x, y2-3r+ 2y and classify each as a local minimum, a local maximum, or a saddle point.

8. Find all critical points for the function f(x,y) = zy + 릎 + ë¦ and classify each as a local minimum, a local maximum, or a saddle point. Ans. Local minimum at (1,1) 9. Use Lagrange multiplier to find the extreme values of the function f(x, y)y, subject to the constraint z2 + y 1. Ans. Mazimum $, Minimum -1