I'm having trouble with the following question about local maxima and minima.
Any help is appreciated. Thanks.
Show that if $a > b > c > 0$ than the function
$f(x,y,z) = (ax^2 +by^2 +cz^2) e^{-x^2 -y^2 -z^2}$
has two local maxima, one local minimum and four saddle points.