Let $f ( x ) = 4 e ^ { x } + 3 x$

Multiple Choice

Let $f ( x ) = 4 e ^ { x } + 3 x$ Then which of the following is the largest interval, of those listed, for which for all x in that interval?

A) $( - \infty , \infty )$
B) $\left( - \infty , - \ln \frac { 3 } { 4 } \right)$
C) $\left( - \ln \frac { 3 } { 4 } , \ln \frac { 3 } { 4 } \right)$
D) $\left( - \infty , \ln \frac { 3 } { 4 } \right)$
E) $\varnothing$