I have been trying to solve the following problem:
Suppose the function $f:\mathbb R \rightarrow \mathbb R$ has left and right derivatives at $0$.Then at $x=0$, which of the following options is correct?
(a)$f$ must be continuous but may not be differentiable,
(b)$f$ need not be continuous but must be left continuous or right continuous,
(c)$f$ must be differentiable,
(d)if $f$ is continuous then $f$ must be differentiable.
Could someone point me in the right direction.Thanks in advance for your time.