To find the average value of a function $f(x)$ on an interval $[a, b]$, you use the formula:

$f_{\text{ave}} = \frac{1}{b - a} \int_a^b f(x) \, dx$

In this case, $f(x) = x$ and the interval is $[0, 4]$. So, we plug these values into the formula:

$f_{\text{ave}} = \frac{1}{4 - 0} \int_0^4 x \, dx = \frac{1}{4} \int_0^4 x \, dx$

Now, we compute the integral:

[ \int_0^4 x , dx = \left[\frac{x^2}{2}\right]_0^4 = \frac{4^2}{2} - \frac{0^2}{2} = \frac{16