calculs 3

pleas help me this four question and give each answer the questions numbers

11. [-/3 Points] DETAILS SCALCET9 14.8.035. MY NOTES Consider the problem of minimizing the function f(x, y) = x on the curve 9y + x - x = 0 (a piriform). (a) Try using Lagrange multipliers to solve the problem. This answer has not been graded yet. (b) Show that the minimum value is f(0, 0) = 0 but the Lagrange condition Vf(0, 0) = 1Vg(0, 0) is not satisfied for any value of 1. This answer has not been graded yet. (c) Explain why Lagrange multipliers fail to find the minimum value in this case.15. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCET9 14.8.051. MY NOTES ASK YOUR TEACHER Use Lagrange multipliers to find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is a constant c. (Enter the dimensions as a comma-separated list.) C 12 X Need Help? Read It Watch It10. [2/3 Points] DETAILS PREVIOUS ANSWERS SCALCET9 14.7.028. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHE Use a graph or level curves to find the local maximum and minimum values and saddle point(s) of the function. Then use calculus to find these values precisely. (Enter your answers as comma- separated lists. If an answer does not exist, enter DNE.) f ( x, y) = sin(x) + sin(y) + cos(x + y)+ 3, 0sxs_ osys . 4 local maximum value(s) 4 X local minimum value(s) DNE saddle point(s) ( x, y ) = DNE12. [11/14 Points] DETAILS PREVIOUS ANSWERS SCALCET9 14.7.035.EP Consider the following function. f ( x, y ) = x2+ 12+ x 2y+ 9 Find the following derivatives. fx ( x , y ) = 2x + 2 xy fy ( x, y ) = 2y + x 2 Find the critical point. ( x, y ) = 0,0 Find the value of f at this critical point. 9 Find the minimum and maximum of f on each segment of the boundary. minimum maximum y = -1 10 10 X = 1 39/4 DNE X = 1 10 10 X = -1 39/4 DNE X Find the absolute maximum and minimum values of f on the set D. D = ( x, y) |1x/ s 1, ly/ s 1} absolute maximum value 12 absolute minimum value