solve the answers handwritten but please type all the final answers together in the different section after solving. Thanks.

1. [-/1 Points] DETAILS SCALCET9 14.8.003. MY NOTES This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f( x, y) = x2 - y2, x2 + y2 = 36 maximum value minimum value Need Help? Read It 2. [-/1 Points] DETAILS SCALCET9 14.8.009. MY NOTES This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. f( x, y, Z) = 4x + 4y + 32, 2x2 + 2y2+ 322 = 19 maximum value minimum value Need Help? Read It Watch It3. [-/1 Points] DETAILS SCALCET9 14.8.015. This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint. R( x , y, Z , t ) = x+y+z+t, x2+ 2+ 22+ +2 = 81 maximum value minimum value Need Help? Read It Watch It 4. [-/1 Points] DETAILS SCALCET9 14.8.019. Use Lagrange multipliers to find the dimensions (in meters) of a rectangle with perimeter 200 m whose area is as large as possible. (Enter the dimensions as a comma-separated list.) m Need Help? Read It 5. [-/1 Points] DETAILS SCALCET9 14.8.027. Find the extreme values of f on the region described by the inequality. (If an answer does not exist, enter DNE.) (( x , y ) = x2 + y2 + 8x - By, x2 + 12 = 81 maximum minimum Need Help? Read It Watch It6. [-/1 Points] DETAILS SCALCET9 14.8.028.EP. Consider the following function on the region described by the inequality. f( x, y) = 2x2 + 3y2 - 4x - 2, g(x, y) = x2 + yz = 16 Find the gradient of f. VA(x, y ) = Find the critical point of f that lies in the given region. ( x, y ) = Find the points on the boundary of the region such that V = AVg. (Order your answers from smallest to largest x, then from smallest to largest y.) ( x, y ) = ( x, y) = Find the extreme values of fon the region described by the inequality. (If an answer does not exist, enter DNE.) maximum minimum Need Help? Read It7. [-/1 Points] DETAILS SCALCET9 14.8.033. Find the extreme values of f subject to both constraints. (If an answer does not exist, enter DNE.) f( x, y, z) = yz + xy; xy = 1, yz + zz = 81 maximum minimum Need Help? Read It Watch It 8. [-/1 Points] DETAILS SCALCET9 14.8.043. Use Lagrange multipliers to find the points on the cone z? = x2 + y that are closest to the point (12, 2, 0). smaller z-value ( x, y, Z ) = larger z-value ( x, y, Z ) = Need Help? Read It Watch It 9. [-/1 Points] DETAILS SCALCET9 14.8.048. Use Lagrange multipliers to find the dimensions of the box with volume 125 cm that has minimal surface area. (Enter the dimensions (in centimeters) as a comma separated list.) Need Help? Read It10. [-/1 Points] DETAILS SCALCET9 14.8.054. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Suppose a package in the shape of a rectangular box can be mailed by a ceratin postal service if the sum of its length and girth (the perimeter of a cross-section perpendicular to the length) is at most 114 inches. Use Lagrange multipliers to find the length, width, and height of the package (in inches) with largest volume that can be mailed. (Enter the dimensions as a comma separated list.) length girth in. Need Help? Read It