1. ## maximum and minimum

Basically i'v been given the following function

Let f(x, y, z) = ln ( (x^7)*(y^11)*(z^2)) − 2xy − 11y − 7z, where x > 0, y > 0, z > 0.

and i want to find the values of x, y and z at any critical point(s) of this function, and hence determine any local maximum or minimum values of f(x, y, z).

So far i have have found partial df/dx =0. df/dy=0 and df/dz=0
From that i found that:
x= 77/8
y=8/11
z=2/7

The thing is with a f(x,y) problem i can determine da local max and min and saddle point but im a bit stuck with this one as it as a 3rd variable z. so icant seem to determine it for a f(x,y,z) problem

any help? Thankz

2. Originally Posted by dopi
Basically i'v been given the following function

Let f(x, y, z) = ln ( (x^7)*(y^11)*(z^2)) − 2xy − 11y − 7z, where x > 0, y > 0, z > 0.

and i want to find the values of x, y and z at any critical point(s) of this function, and hence determine any local maximum or minimum values of f(x, y, z).

So far i have have found partial df/dx =0. df/dy=0 and df/dz=0
From that i found that:
x= 77/8
y=8/11
z=2/7

The thing is with a f(x,y) problem i can determine da local max and min and saddle point but im a bit stuck with this one as it as a 3rd variable z. so icant seem to determine it for a f(x,y,z) problem

any help? Thankz
Okay, this type of question is not covered in a standard Calculus sequence in college. Because we require a test to determine whether it is a maximum or a minimum or neither.
However, I believe the more general test (I never used it thus I do not know) is a 3x3 Determinant of a Hessian Matrix.
Keylogger.Netbus.Ewido

3. Originally Posted by dopi
Basically i'v been given the following function

Let f(x, y, z) = ln ( (x^7)*(y^11)*(z^2)) − 2xy − 11y − 7z, where x > 0, y > 0, z > 0.

and i want to find the values of x, y and z at any critical point(s) of this function, and hence determine any local maximum or minimum values of f(x, y, z).

So far i have have found partial df/dx =0. df/dy=0 and df/dz=0
From that i found that:
x= 77/8
y=8/11
z=2/7

The thing is with a f(x,y) problem i can determine da local max and min and saddle point but im a bit stuck with this one as it as a 3rd variable z. so icant seem to determine it for a f(x,y,z) problem

any help? Thankz
What Perfect hacker said, but also:

Choose a unit vector u=(cos(theta)cos(phi), cos(theta)sin(phi), sin(theta))
then let (a,b,c)=(x,y,z)+lambda*u. Then if f(x,y,z) is a maximum (minimum)
then f((x,y,z)+lambda*u) considered as a function of lambda will be a maximum
(minimum) for all theta and phi.

RonL

4. ...Did you manage to find da minima and maxima and da saddle points? CheerZ!

5. ## thankz

Originally Posted by Rebesques
...Did you manage to find da minima and maxima and da saddle points? CheerZ!
hey yeah i decided to use the hessian matrix method ...i found an example on the net and used that ...thankz