Question 222·Hard·Nonlinear Functions

For $x \ge 0$, the functions are defined as follows.

I. $f(x)=4^{-(x+1)}$

II. $g(x)=\dfrac14\,4^{-x}$

Which of these equations displays, as a constant or coefficient, the maximum value of the function it defines, where $x \ge 0$?