Let f(x, y) = x² y⁴ + x⁴ - 6y⁸ if (x, y) = (0, 0) and 0 otherwise. Show that ∂f/∂x(0, 0) and ∂f/∂y(0, 0) exist.
a) They both exist and are finite.
b) They both exist but are infinite.
c) Only one exists and is finite.
d) None of them exist.