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.

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The Answer of 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.

Let f(x,y)=ax2−2axy+4y2−bxf ( x , y ) = a x ^ { 2 } - 2 a x y + 4 y ^ { 2 } - b xf(x,y)=ax2−2axy+4y2−bx

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