## anonymous 5 years ago LaGrange Multipliers Help Please!

1. 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!

2. 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 $\lambda$.

3. anonymous

What about the partial derivative with respect to z?

4. anonymous

there are two methods to working this? You can find it also and by finding the z

5. 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

6. 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.

7. anonymous

How do you solve simultaneously when we habe xz i the first eqn and yz in the second?

8. anonymous

but we have λ in both

9. anonymous

Yes, and...

10. anonymous

lol

11. anonymous

λ- (y+2z/yz)=0 equation 1 λ- (x+2z/xz)=0 equation 2

12. anonymous

or you could solve by letting λ= λ

13. anonymous

Disclaimer, this is how I would attempt this question based on how i was taught

14. anonymous

Haha! I'm only kidding!

15. anonymous

do u agree or not?

16. anonymous

I'll quickly give it a go and see what I get...

17. anonymous

well its not quiet... clear so I need to get help