While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_0$ to be a minima are:

1. $f’(x_0) > 0$ and $f’’(x_0)=0$
2. $f’(x_0) < 0$ and $f’’(x_0)=0$
3. $f’(x_0) = 0$ and $f’’(x_0)<0$
4. $f’(x_0) = 0$ and $f’’(x_0)>0$