Let $f(x,y,z)=e^x(xy-y^2-z^2)$ and let A be the critical point nearest to the origin while B is the critical point furthest from the origin
Find the x.y and z coordinates of A and B
What i did
For A, i first find the partial derivatives of the original function then equating it to 0
$f_{x}=0$
$f_{y}=0$
$f_{z}=0$
which gives a critical point of (0,0,0).
From here i let A be$$(x,y,z) $$ Then using distance formula i let the distance of A to the origin be
$$\sqrt{(x^2-0)+(y^2-0)+(z^2-0)}$$
and do a partial derivative of this function to find the minimum point of this function
and equating it to 0 to find (x.y.z) hence finding out the coordinates of A which
turns out to be(0,0,0) which is the correct answer.
However, when i tried to find B using the same method as above, the method above dosent
work. Could anyone explain whether could i use the method above to find B. And if it is
not possible, then how to find B? Thanks