Near $x = 0$, how does $f(x) = - 3 x + e^{x}$ behave?

Explanation

1. 01

   $f'(x) = e^{x} - 3$, so $f'(0) = -2$.

2. 02

   A positive derivative means the function is rising there, a negative one falling, and 0 a turning or flat point.