Consider the function f(x, y) = x^2 - y^2 + 5.

(a) (1 pt) Compute the partial derivatives @f/@x (x, y) and @f/@y (x, y).

(b) (2 pts) Is the function f(x, y) differentiable at every point? Explain.

(c) (2 pts) Determine an equation for the tangent plane to the graph z = f(x, y) at

the point (1, 1, f(1, 1)).

(d) (5 pts) Show that the intersection between the graph z = f(x, y) and the plane

found in part (c) consists of two curves meeting at a point, and find parametric

equations for those curves.