8 A surface \(S\) has equation \(z = 8 y ^ { 3 } - 6 x ^ { 2 } y + 60 x y - 15 x ^ { 2 } + 186 x - 150 y - 100\).
- (a) Find any stationary points of the section of \(S\) given by \(y = - 3\).
(b) Find any stationary points of the section of \(S\) given by \(x = - 1\). - Show that the surface \(S\) has a least one saddle point.
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