True or false: continuity and differentiability

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   Every differentiable function is continuous.

2. Statement is true

   No

   Statement

   Every continuous function is differentiable.

3. Statement is true

   Yes

   Statement

   The converse of the first statement is not true.

4. Statement is true

   Yes

   Statement

   Differentiability is the stronger condition.

5. Statement is true

   Yes

   Statement

   A function can be continuous without being differentiable.

Explanation