Let (x, y) be a continuous function on a domain D in R 2 . Determine which of the following statements are true: (a) If

Let ƒ(x, y) be a continuous function on a domain D in R². Determine which of the following statements are true:

(a) If D is closed and bounded, then f takes on a maximum value on D. (b) If D is neither closed nor bounded, then f does not take on a maximum value of D. (c) f(x, y) need not have a maximum value on the domain D defined by 0 x 1,0 y 1. (d) A continuous function takes on neither a minimum nor a maximum value on the open quadrant {(x, y) : x > 0,y>0}