The continuous function $$f(x, y)$$ is said to have saddle point at $$(a, b)$$ if

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$ $$f_{xy}^2 - {f_{xx}}{f_{yy}} > 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = {f_y}\left( {a,\,b} \right) = 0$$ $$f_{xy}^2 - {f_{xx}}{f_{yy}} < 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$ $$f_{xy}^2 - {f_{xx}}{f_{yy}} > 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0,$$ $${f_{xx}}$$ and $${f_{yy}} < 0$$ at $$(a, b)$$

$${f_x}\left( {a,\,b} \right) = 0,{f_y}\left( {a,\,b} \right) = 0$$ $$f_{xy}^2 - {f_{xx}}{f_{yy}} = 0\,\,$$ at $$(a, b)$$

GATE 1998 Civil Engineering PYQ — Engineering Mathematics

GATE 19981998PYQMCQanswer keyexplanation sooneasy

Engineering Mathematics · Calculus (CE)

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Recurring concept

Calculus (CE) has appeared in GATE Civil Engineering 96 times across 28 years (2018, 2022, 2023, 2024, 2025, ...).