# 微積分證明問題

A function f(x) : [a,b] R satisfies a Lipschitz condition if there exists

a constant L>0 such that 1f(x)-f(y)1<=L1x-y1 whenever x and y in [a,b].

prove that :

(a) a function satisfies a Lipschitz condition on [a,b] is continuous

on [a,b]

(b)if 1f'(x)1<=M for all x屬於[a,b] , then it satisfies a Lipschitz condition on [a,b]