# Real analysis : Lipschitz Criterion

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A function f:A->R is Lipschitz on A if there exists an M>0 such that Absolute value of f(x)-f(y)/x-y <=M for all x,y belong to A. show that if f is differentiable on a closed interval [a,b] and if f' is continous on [a,b] then f is Lipschtiz on [a,b].

Geomtrically speaking, a function f is Lipschitz if there is a uniform bound on the magnitude of the slopes of lines drawn through any two points on the graph of f.

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a function f:A->R is Lipschitz on A if there exists an M>0 such that Absolute value of f(x)-f(y)/x-y <=M for all x,y belong to A. show that if f is differentiable on a closed interval ...

#### Solution Summary

The Lipschitz criterion is investigated.

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