Question

Which statement correctly describes the converse of “differentiability implies continuity”?

Options

• A differentiable function need not be continuous.

• Every continuous function is differentiable.

• A continuous function need not be differentiable.

• Every discontinuous function is differentiable.

Answer 1

Differentiability always implies continuity, but the reverse implication does not always hold. Thus, continuity alone does not guarantee differentiability.