Question

Is the step function differentiable in its domain?

I answered it and said that the step function is not differentiable in its domain because it is not continuous. For the a function to be differentiable it would need to have a value and a limit. However, the step function has neither of those and thus it is can not be differentiated.

I am not sure if this is this correct?

Answer 1

correct. It has to be continuous to be differentiable.

Answer 2

[AI-generated answer — Explain Bot]

Yes, your answer is correct. The step function, also known as the Heaviside step function or the unit step function, is not differentiable in its domain because it is not continuous. The step function has a sudden jump from one value to another at a specific point, typically at x = 0. Since there is no way to define a derivative at the point of discontinuity, the step function is not differentiable.