Section 14.8 5. Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y)=x² − y² /2 subject to the constraint 3x² + y² = 4. 6. Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y,z)=yz-xz subject to the constraints yz=4 and x²+z² = 1. 7. Use Lagrange multipliers to find the maximum and minimum values of the function f(x,y) = x² + y² −4x+6y on the region described by the inequality x²+2 ≤9. 8. Use Lagrange multipliers to find the shortest distance from the point (0, 1, -4) to the plane x-3y+6z=0. You had to solve this same problem using the Second Derivative Test earlier in this assignment.