Question

Please help me finish these two problems, I really have no way. Thank you for your patience! thank you！

3. -/2 points SCalcET7 14.8.004. Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x, ) = 6x + 6y; x2 + y2 = 18 maximum minimum Need Help? Talk to a Tutor Show My Work (Optional) 4. -12 points ScalcET7 14.8.005. Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x, y) = y2 - x2; 1x2 + y2 = 25 maximum minimum Need Help? Talk to a Tutor Show My Work (Optional)

Answer 1

22 (3) finis) = 62464, gen,y)= x²742_18 If = <6, 67, ag=<22, 24) et a be ine. Lagrangian multiplier Then &f=nog. ... >> <6,67 = 2322,27) → 272 = 6 => x= { 274 = 6 : = y = 3/ .. Now, x²4 y2 = 18 = 2 + 2 = 18 >>721 on = $1, ei 2= 33, y=3. : Noi f(3,37 = 63 +6735 36 63,-3) = 6.6–37 +6(-3) =-36. e so manimum = 136] minimum = T-36] (4) f(x,y)= y²_n² geniy) = 2 ²74²-25 vf = <-27, 2y), og = < , 27) ... of. = 209 = (-24,27) = 2<3,2y> => –22 = 72 = (2+4)* = 0. = 334 ... and 2y = 924 = 2(2-3y =o. asmod. In this case we have nzo, y=0; which does not satisfies . . gen,y)=0. не са.. Manimum DNE) Miniman IDNE]