Q1.2 A real-valued function f x (x 2 R) is said to be Lipschitz continuous if there exists a real constant L > 0, for

Q1.2 A real-valued function f ¹xº (x 2 R) is said to be Lipschitz continuous if there exists a real constant L > 0, for any two points x1 2 R and x2 2 R, where f ¹x1º ???? f ¹x2º

 L jx1 ???? x2 j always holds. If f ¹xº is differentiable, prove that f ¹xº is Lipschitz continuous if and only if f 0¹xº

 L holds for all x 2 R.