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

Question

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

anonymous · Answer

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?