Question

Which of the following statements is true?

• A. A continuous function is an increasing function.
• B. An increasing function is continuous.
• C. A continuous function is differentiable.
• D. A differentiable function is continuous.

Answer 1

Answer: (D)

A differentiable function is continuous.

Answer 2

A differentiable function is continuous, this statement is true because if a function is differentiable at a point, it implies that it is also continuous at that point. However, the converse is not necessarily true; a continuous function may not be differentiable at every point.

So, the correct option is (D): A differentiable function is continuous.