anonymous
  • anonymous
Use Lagrange multipliers to identify the critical points of f subject to the given constraints. (Order the critical points from smaller x to larger x. If the x-values are the same, order the points from smaller y to larger y and finally from smaller z to larger z. Enter NONE in any unused answer blanks.) f(x, y, z) = x + y + z, y2 – x2 = 4, x + 2z = 5
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
well first you to know that \[Gradf=\lambda Grad(g)+\lambda Grad(h)\] There are two different lamdas by the way. One is labeled lamda 1 and the other is lamda 2. So take partials of f with respect to x y and z. Which is 1 for each of them. Hence, <1,1,1>=lamdaone<-2x,2y,0>+lamdatwo<1,0,2> Now you set them equal to each other: CAn you do the rest?

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