A function $f$ is said to satisfy Lipscitz condition on $D$ if there exists $M>0$ such that for every $x_1,x_2$ belonging to $D$ we have $$|f(x_1)-f(x_2)|\leq M|x_1-x_2|.$$ Now, what is the geometric interpretation of this thing? Does this mean that slope of chord joining any $2$ points on the curve $y=f(x)$ is bounded. Does this imply that derived function $f'$ of $f$ is bounded on $D$ (provided derivative exists on $D$)? Can it be understood with the help of diagram geometrically? I had heard some concept of double cone for this thing. Can someone explain that, too?
2026-04-13 12:03:46.1776081826
What is the geometrical interpretation of Lipschitz condition?
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