Let $f ( x , y ) = a x ^ { 2 } - 2 a x y + 4 y ^ { 2 } - b x$

Short Answer

Let $f ( x , y ) = a x ^ { 2 } - 2 a x y + 4 y ^ { 2 } - b x$ , where a, b are any positive numbers with a $\gt$ 4.
Find the minimum value of a such that the critical point will be a saddle point.