3 The function \(w = \mathrm { f } ( x , y , z )\) is given by \(\mathrm { f } ( x , y , z ) = x ^ { 2 } y z + 2 x y ^ { 2 } z + 3 x y z ^ { 2 } - 24 x y z\), for \(x , y , z \neq 0\).

1. (a) Find
   • \(\mathrm { f } _ { x }\),
   • \(\mathrm { f } _ { y }\),
   • \(\mathrm { f } _ { z }\).
     (b) Hence find the values of \(a , b , c\) and \(d\) for which \(w\) has a stationary value when \(d = \mathrm { f } ( a , b , c )\).
   • You are given that this stationary value is a local minimum of \(w\). Find values of \(x , y\) and \(z\) which show that it is not a global minimum of \(w\).