While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_{0}$ to be a minima are:
(A) $f^{\prime}\left(x_{0}\right)>0$ and $f^{\prime \prime}\left(x_{0}\right)=0$
(B) $f^{\prime}\left(x_{0}\right)<0$ and $f^{\prime \prime}\left(x_{0}\right)=0$
(C) $f^{\prime}\left(x_{0}\right)=0$ and $f^{\prime \prime}\left(x_{0}\right)<0$
(D) $f^{\prime}\left(x_{0}\right)=0$ and $f^{\prime \prime}\left(x_{0}\right)>0$

Question ID - 156153 | SaraNextGen Top Answer

While minimizing the function $f(x)$, necessary and sufficient conditions for a point, $x_{0}$ to be a minima are:
(A) $f^{\prime}\left(x_{0}\right)>0$ and $f^{\prime \prime}\left(x_{0}\right)=0$
(B) $f^{\prime}\left(x_{0}\right)<0$ and $f^{\prime \prime}\left(x_{0}\right)=0$
(C) $f^{\prime}\left(x_{0}\right)=0$ and $f^{\prime \prime}\left(x_{0}\right)<0$
(D) $f^{\prime}\left(x_{0}\right)=0$ and $f^{\prime \prime}\left(x_{0}\right)>0$