Answer
(a) the statement $\frac{{\partial D}}{{\partial y}}{|_A} > \frac{{\partial D}}{{\partial y}}{|_B}$ is true.
(b) the statement $\frac{{\partial D}}{{\partial x}}{|_C} > 0$ is true.
(c) the statement $\frac{{\partial D}}{{\partial y}}{|_C} > 0$ is false.
Work Step by Step
(a) We move up vertically from point $A$ and notice that $\frac{{\partial D}}{{\partial y}}{|_A} > 0$
And since $\Delta D = 0$ for point $B$, we have $\frac{{\partial D}}{{\partial y}}{|_B} \approx \frac{{\Delta D}}{{\Delta y}}{|_B} = 0$.
Thus, the statement $\frac{{\partial D}}{{\partial y}}{|_A} > \frac{{\partial D}}{{\partial y}}{|_B}$ is true.
(b) Consider point C.
Moving to the left horizontally we get $\Delta D > 0$ and $\Delta x > 0$.
So $\frac{{\partial D}}{{\partial x}}{|_C} \approx \frac{{\Delta D}}{{\Delta x}}{|_C} > 0$
Thus, the statement $\frac{{\partial D}}{{\partial x}}{|_C} > 0$ is true.
(c) Consider point C.
Moving up vertically we get $\Delta D < 0$ and $\Delta y > 0$, so $\frac{{\partial D}}{{\partial y}}{|_C} \approx \frac{{\Delta D}}{{\Delta y}}{|_C} < 0$
Thus, the statement $\frac{{\partial D}}{{\partial y}}{|_C} > 0$ is false.
