Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be any twice differentiable function such that its second derivative is continuous and $$\frac { d f ( x ) } { d x } \neq 0 \text { for all } x \neq 0$$ If $$\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { 2 } } = \pi$$ then (A) for all $x \neq 0 , \quad f ( x ) > f ( 0 )$. (B) for all $x \neq 0 , \quad f ( x ) < f ( 0 )$. (C) for all $x , \frac { d ^ { 2 } f ( x ) } { d x ^ { 2 } } > 0$. (D) for all $x , \frac { d ^ { 2 } f ( x ) } { d x ^ { 2 } } < 0$.
Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be any twice differentiable function such that its second derivative is continuous and
$$\frac { d f ( x ) } { d x } \neq 0 \text { for all } x \neq 0$$
If
$$\lim _ { x \rightarrow 0 } \frac { f ( x ) } { x ^ { 2 } } = \pi$$
then\\
(A) for all $x \neq 0 , \quad f ( x ) > f ( 0 )$.\\
(B) for all $x \neq 0 , \quad f ( x ) < f ( 0 )$.\\
(C) for all $x , \frac { d ^ { 2 } f ( x ) } { d x ^ { 2 } } > 0$.\\
(D) for all $x , \frac { d ^ { 2 } f ( x ) } { d x ^ { 2 } } < 0$.