The Speed the Average Never Sees

A survey drone climbs straight up from its launch pad. Its height above the pad, $t$ seconds after take-off, is

$s(t) = 2t(15 - t) + 9$

with $s$ in metres and $t$ in seconds, valid for $0 \le t \le 7$.

The flight log happily reports the drone's average climb rate over a stretch of the flight. The camera's stabiliser cannot use that. It needs the instantaneous rate at the exact moment the shutter opens.

Using the limit definition

$s'(t) = \lim_{h \to 0} \frac{s(t + h) - s(t)}{h}$

find the instantaneous rate at which the drone's height is changing at $t = 4$ seconds.

Give an exact value.