What does it mean for a function to be differentiable on an open interval? On a closed interval?

Step 1 of 3:

In this question, we have to define the mean for a function to be differentiable on an open interval? On a closed interval?

Step 2 of 3:

Continuous functions are constantly characterized by the closed interval, and differentiable functions, dependable on open interims. For example, suppose that we need to demonstrate a property of a continuous function, it would go as "Let f be a consistent capacity on [a,b]⊂R .. for a differentiable function it would be (a,b).

At that point is the derivative of the function differentiable on the closed interval [1,4] or open interval (1,4).