Derivative as a limit: numerical

Jude wants to find the derivative of

h (x) = 12 \ln (x)

at the point

x = 4

His table below shows the average rate of change of

h

over the intervals

[x, 4]

[4, x]

for

x

-values that get increasingly closer to

4

$x$ ‍	Interval	Average rate of change, $\frac{h (x) - h (4)}{x - 4}$ ‍
$3.9$ ‍	$[3.9, 4]$ ‍	$3.0381$ ‍
$3.99$ ‍	$[3.99, 4]$ ‍	$3.0038$ ‍
$3.999$ ‍	$[3.999, 4]$ ‍	$3.0004$ ‍
$4.001$ ‍	$[4, 4.001]$ ‍	$2.9996$ ‍
$4.01$ ‍	$[4, 4.01]$ ‍	$2.9963$ ‍
$4.1$ ‍	$[4, 4.1]$ ‍	$2.9631$ ‍

From the table, what does the derivative of $h (x) = 12 \ln (x)$ ‍ at $x = 4$ ‍ appear to be?

Calculus, all content (2017 edition)