Question: Consider the function: F (x1, x2, y) = x1^2 − x2^2 + y^3.

(a) Show that the equation F (x1, x2, y) = 0 defines y as an implicit function of x1

and x2 near the point (x1, x2) = (6, 3).

(b) Use the implicit function theorem to compute: ∂y/∂x1 and ∂y/∂x2

at the point (x1, x2) = (6, 3).