2017 TWO(b)

The percentage of seeds germinating depends on the amount of water applied to the seedbed
that the seeds are sown in, and may be modelled by the function:

$P(w)=96\ln (w+1.25)-16w-12$

where $P$ is the percentage of seeds that germinate and
$w$ is the daily amount of water applied (litres per square metre of seedbed), with $0\le w\le 15$.

Find the amount of water that should be applied daily to maximise the percentage of seeds
germinating.

*You must use calculus and show any derivatives that you need to find when solving this
problem.*