Consider the graph of a twice-differentiable function $f\left(x\right)$. Determine whether $f^{\prime }\left(x\right)$ and $f^{\prime }$${}^{\prime }\left(x\right)$ are positive, negative, or zero at point $A$.

$f^{\prime }\left(x\right)$ is positive and $f^{\prime }$${}^{\prime }\left(x\right)$ is zero

$f^{\prime }\left(x\right)$ is zero and $f^{\prime }$${}^{\prime }\left(x\right)$ is positive

$f^{\prime }\left(x\right)$ is positive and $f^{\prime }$${}^{\prime }\left(x\right)$ is negative

$f^{\prime }\left(x\right)$ and $f^{\prime }$${}^{\prime }\left(x\right)$ are both zero