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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 | Toppr 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 $f^{\prime \prime}\left(x_{0}\right)>0$

1 Answer - 5876 Votes

3537

Answer Key : (D) -

$f^{\prime}\left(x_{0}\right)=0$ and $f^{\prime \prime}\left(x_{0}\right)>0$



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