Question

If a function \[f\] is differentiable at a point \[c\], what must be true at that point?

Options

• \[f\] is not continuous at \[c\].

• \[f'(c)=0\].

• \[f\] is continuous at \[c\].

• \[f\] is differentiable only from the left at \[c\].

Answer 1

Differentiability implies continuity at the same point. Thus, if \[f\] is differentiable at \[c\], then \[f\] is continuous at \[c\].