Worldwide soybean production in a given year depends on the average temperature T and the average rainfall R. Scientists estimate that the average temperature is rising at a rate of 0.15◦ C/year and that rainfall is decreasing at a rate of 0.1 cm/year. They also estimate that at current production levels, ∂W/∂T = −2 and ∂W/∂R = 8.
A) What is the significance of the signs of these partial derivatives?
B) Estimate the current rate of change of wheat production, ∂W/∂t.