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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?
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
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