Let $f : \mathbb { R } \longrightarrow ( 0 , \infty )$ be an infinitely differentiable function with $\int _ { - \infty } ^ { \infty } f ( t ) d t = 1$. Pick the correct statement(s) from below. (A) $f ( t )$ is bounded. (B) $\lim _ { | t | \rightarrow \infty } f ^ { \prime } ( t ) = 0$. (C) There exists $t _ { 0 } \in \mathbb { R }$ such that $f \left( t _ { 0 } \right) \geq f ( t )$ for all $t \in \mathbb { R }$. (D) $f ^ { \prime \prime } ( a ) = 0$ for some $a \in \mathbb { R }$.
Let $f : \mathbb { R } \longrightarrow ( 0 , \infty )$ be an infinitely differentiable function with $\int _ { - \infty } ^ { \infty } f ( t ) d t = 1$. Pick the correct statement(s) from below.\\
(A) $f ( t )$ is bounded.\\
(B) $\lim _ { | t | \rightarrow \infty } f ^ { \prime } ( t ) = 0$.\\
(C) There exists $t _ { 0 } \in \mathbb { R }$ such that $f \left( t _ { 0 } \right) \geq f ( t )$ for all $t \in \mathbb { R }$.\\
(D) $f ^ { \prime \prime } ( a ) = 0$ for some $a \in \mathbb { R }$.