Using Lipschitz continuity on open intervals

[Calabi_Yau]

Homework Statement

Prove whether f(x) = x^3 is uniformly continuous on [-1,2)

Homework Equations

The Attempt at a Solution

I used Lipschitz continuity. f has a bounded derivative on that interval, thus it implies f is uniformly continuous on that interval.

But as it is not a closed interval, I am not sure I can use that approach. Any insight would be appreciated. Thanks.

 

[Dick]

Homework Statement

Prove whether f(x) = x^3 is uniformly continuous on [-1,2)

Homework Equations

The Attempt at a Solution

I used Lipschitz continuity. f has a bounded derivative on that interval, thus it implies f is uniformly continuous on that interval.

But as it is not a closed interval, I am not sure I can use that approach. Any insight would be appreciated. Thanks.

Maybe you should look at the definition of uniform continuity. I'm not sure why you are concerned about whether the interval is closed or not.