anonymous
  • anonymous
LaGrange Multipliers Help Please!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
f(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
  • anonymous
Step 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
  • anonymous
What about the partial derivative with respect to z?

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anonymous
  • anonymous
there are two methods to working this? You can find it also and by finding the z
anonymous
  • anonymous
This is my attempt, does not necessarily have to be correct. F( x,y,λ) = f(x,y)- λ[ g(x,y)- c] Fx= y+2z-λyz Fy= x+2z-λxz Fy=0 x+2z-λxz=0 λ= x+2z/xz Fx=0 y+2z-λyz=0 λ= y+2z/yz solve simultaneously
anonymous
  • anonymous
Continue from here... Also Fλ= xyz, that why it is not necessary to find it because it give us the constraint, which already given.
anonymous
  • anonymous
How do you solve simultaneously when we habe xz i the first eqn and yz in the second?
anonymous
  • anonymous
but we have λ in both
anonymous
  • anonymous
Yes, and...
anonymous
  • anonymous
lol
anonymous
  • anonymous
λ- (y+2z/yz)=0 equation 1 λ- (x+2z/xz)=0 equation 2
anonymous
  • anonymous
or you could solve by letting λ= λ
anonymous
  • anonymous
Disclaimer, this is how I would attempt this question based on how i was taught
anonymous
  • anonymous
Haha! I'm only kidding!
anonymous
  • anonymous
do u agree or not?
anonymous
  • anonymous
I'll quickly give it a go and see what I get...
anonymous
  • anonymous
well its not quiet... clear so I need to get help

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