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Previous Year Question (PYQs)

Let $f(x,y) = x^3 + y^3$ for all $(x,y) \in \mathbb{R}^2$. Then




Solution

$f_x = 3x^2$ $f_y = 3y^2$ At (0,0) → critical point Second derivatives: $f_{xx} = 6x$, $f_{yy} = 6y$ At (0,0) → 0 Function changes sign around origin → saddle point

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