LaGrange Multipliers Help Please!

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LaGrange Multipliers Help Please!

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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!
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 \[\lambda\].
What about the partial derivative with respect to z?

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

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