Question

$f\left(c\right)$ is a maximum value of $f\left(x\right)$, if-

• A. $f^{\prime }\left(c\right)=0$, $f^{\prime \prime }\left(c\right)>0$
• B. $f^{\prime }\left(c\right)=0$, $f^{\prime \prime }\left(c\right)<0$
• C. $f^{\prime }\left(c\right)\ne 0$, $f^{\prime \prime }\left(c\right)=0$
• D. $f^{\prime }\left(c\right)<0$, $f^{\prime \prime }\left(c\right)>0$

Answer 1

The correct option is B $f^{\prime }\left(c\right)=0$, $f^{\prime \prime }\left(c\right)<0$

$f\left(c\right)$ is the maximum value of $y=f\left(x\right)$ if
$f^{\prime }\left(c\right)=0$ and $f^{\prime \prime }\left(c\right)<0$.