A curve is defined by the equation $y=g(x)$. It is known that the curve has a point of inflection at $x=-4$. Given that $g^{\prime }(-4)=k$ and $g^{\prime \prime }(-4)=m$, where $k$ and $m$ are constants, identify which of the following statements must be true:

$$g^{\prime }(-4)=0$$ $$g^{\prime \prime }(-4)=0$$ $$g^{\prime }(-4)\ne 0$$ $$g^{\prime \prime }(-4)>0$$