Let $f ( x ) = x - 4 e ^ { x }$

Multiple Choice

Let $f ( x ) = x - 4 e ^ { x }$ Then which of the following is the largest interval, of those listed, for which $f ^ { \prime } ( x ) < 0$ for all x in that interval?

A) $( - \infty , \infty )$
B) $( - \infty , - \ln 4 )$
C) $( - \ln 4 , \ln 4 )$
D) $( - \ln 4 , \infty )$
E) $\varnothing$