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anonymous
 5 years ago
LaGrange Multipliers Help Please!
anonymous
 5 years ago
LaGrange Multipliers Help Please!

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0f(x,y,z) = xy + 2xz + 2yz Constraint xyz = 32 I know the steps of finding the partial derivatives but I get stuck after that. Do I also need to find the Partial derivative of \[\lambda\]  Having 3 variables is proving difficult for me! Any help as to how I can solve it? Thanks!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Step 1 Fx & Fy i.e differentiate with respect to x , Fx ,then differentiate with respect to y, Fy. Step 2 F x=0 and Fy=0 ( solve simultaneously ) Step 3 Substitute in the constraint to get the critical points (x,y,z). Solve for x in terms of \[\lambda\].

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What about the partial derivative with respect to z?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0there are two methods to working this? You can find it also and by finding the z

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0This is my attempt, does not necessarily have to be correct. F( x,y,λ) = f(x,y) λ[ g(x,y) c] Fx= y+2zλyz Fy= x+2zλxz Fy=0 x+2zλxz=0 λ= x+2z/xz Fx=0 y+2zλyz=0 λ= y+2z/yz solve simultaneously

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Continue from here... Also Fλ= xyz, that why it is not necessary to find it because it give us the constraint, which already given.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How do you solve simultaneously when we habe xz i the first eqn and yz in the second?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but we have λ in both

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0λ (y+2z/yz)=0 equation 1 λ (x+2z/xz)=0 equation 2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0or you could solve by letting λ= λ

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Disclaimer, this is how I would attempt this question based on how i was taught

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Haha! I'm only kidding!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'll quickly give it a go and see what I get...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0well its not quiet... clear so I need to get help
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