Necessary & Sufficient Conditions for Minima | GATE CE 2015 Set 2 Q11

Civil Engineering > GATE 2015 SET-2 > Calculus

While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ 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 $f''(x_0) > 0$

Correct : d

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