engineering recuitment GATE CE 2023-24 Test Series Engineering Mathematics Calculus Differentiability
Let \({\rm{f}}\left( {{\rm{x}},{\rm{y}}} \right) = \frac{{{\rm{a}}{{\rm{x}}^2} + {\rm{b}}{{\rm{y}}^2}}}{{{\rm{xy}}}}\), where a and b are constants. If \(\frac{{\partial {\rm{f}}}}{{\partial {\rm{x}}}} = \frac{{\partial {\rm{f}}}}{{\partial {\rm{y}}}}{\rm{\;}}\) at x = 1 and y = 2, then the relation between a and b is
1
\({\rm{a}} = \frac{{\rm{b}}}{4}\)
2
\({\rm{a}} = \frac{{\rm{b}}}{2}\)
3
a = 2b
4
a = 4b