LaGrange Multiplies

[engineertobe]

Q:
Using Lagrange multipliers, find the maximum and minimum values of the function f(x

y

z)=x−5z subject to the constraint 2x^2+9y^2+z^2−5=0.


I have been taking the partial derivatives but when I am solving for the different valuesI am getting equations which aren't mathematically true! Please help!

 

[tkhunny]

You'll have to demonstrate.

You may need the requirement that \(\displaystyle \lambda \ne 0\). That should help you with 'y'.

 

[engineertobe]

1=λ2x
0=λ18y
-5=λ2z

so

x=1/2λ
y=0
z=-5/2λ

λ=sqrt(1.35)

Then I proceeded to find the pts and values, but thats wrong!

 

[galactus]

\(\displaystyle \frac{1}{4x}=\frac{-5}{2z}\)

\(\displaystyle z=-10x\)