Local maxima, minima, and saddle points
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Then the function what?
I reckon there is more to it than the second derivative test and algebra. However, I can't think of the right idea yet.
What working out have you done so far?
(Original post by Neilding91)
Show that if a>b>c>0 then the function:
Can someone please help me with this question I have spent hours on it and have made no progress..
2. Solve them simoultaneously
a) first solution is trivial (0,0,0)
b)then arrange the first equation to x^2 and substitute into the others
You will get y=0 and z=0 so x^2=1
this gives 2 soluutions
c) because of simmetry similary to above for y and z you will get more 4 solutions
So you have 7 stationary points
3. Determine the second partial derivatives
4. Create the Hessian matrix for each given (x,y,z) value (7 matrices)
5. For every matrix:
Calculate the eigen values
a) When the matrix positive definite (all eigen value is positive)
then there minimum at that point where the matrix was calculated
b) when the matrix negative definite there is maximum
c) and when the matrix has both negative and positive eigen values or zero
then there is a saddle at the given point
I haven't tried it yet but I cant see why brute force wouldn't work in trying to calculate the maxima and minima etc.
EDIT: as ztbor did. Sounds like a reasonable method.
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