Science:Math Exam Resources/Courses/MATH110/December 2012/Question 02 (e)/Solution 1

A function is non-differentiable if it has a vertical tangent or a sharp corner (cusp). A function is continuous if it can be drawn in one go without lifting your pencil. It is possible to draw a continuous function with one (or multiple!) of the non-differentiable properties just listed:

So a function can be continuous, without necessarily being differentiable. Thus the statement is false.