The discussion centers on the uniform continuity of the function f(x) = x^3 on the interval [-1, 2). It is established that Lipschitz continuity can be applied since the function has a bounded derivative on this interval, confirming that f is uniformly continuous despite the interval being open. The concern regarding the closed nature of the interval is addressed, emphasizing that it does not affect the application of Lipschitz continuity in this case.
PREREQUISITESMathematics students, particularly those studying real analysis, educators teaching calculus concepts, and anyone interested in the properties of continuous functions.
Calabi_Yau said: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.