GATE Civil Engineering (CE) 2015 Shift 2 Solved Paper

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Question : 11 of 65

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While minimizing the function f(x), necessary and sufficient conditions for a point, x₀ to be a minima are:

$f^{′} (x_{0}) > 0\:and\:f^{″} (x_{0}) = 0$
$f^{′} (x_{0}) < 0\:and\:f^{″} (x_{0}) = 0$
$f^{′} (x_{0}) = 0\:and\:f^{″} (x_{0}) = 0$
$f^{′} (x_{0}) = 0\:and\:f^{″} (x_{0}) > 0$

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