6. The fish population $P$ in a certain lake depends on the average water temperature $T$ and the lake's pH level $H$. Ecologists estimate that the average water temperature is increasing at a rate of 0.2°C/year and the pH level is decreasing at a rate of 0.03 per year. They also estimate that, at the current population level, $\frac{\partial P}{\partial T} = -5$ and $\frac{\partial P}{\partial H} = 6$.
(a) What is the significance of the signs of these partial derivatives?
(b) Estimate the current rate of change of the fish population, $\frac{dP}{dt}$.
