Consider the functions (x, y) = x - y and g(x, y) = x + y. (a)

Consider the functions

ƒ(x, y) = x² - y² and g(x, y) = x² + y².

(a) Show that both functions have a critical point at (0, 0). 

(b) Explain how ƒ and g behave differently at this critical point.