Question: Are the following functions Lipschitz continuous on the indicated sets? (Incidentally, all of these examples are scalar-valued functions; vector-valued functions would not pose any additional difficulties except for the need to examine more components.)

(a) (x + 2)^1/3 on the interval [1, 1]? On [, 1]?

(b) (x² + 2)^1/3 on the interval [1, 1]? On [, 1]?

(c) (2x³ + 1)^1/3 on the interval [1, 1]? On [, 1]?

(d) (2x⁴ + 1)^1/3 on the interval [1, 1]? On [, 1]?