2
$\begingroup$

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.

1 Answers 1

2

The function $f(x)=|x|$ should guide you towards the right answer. Also, if $f(x)$ is left-differentiable, what can you say about the left limit?

  • 0
    Then i think option $(b)$ is the right choice.2012-12-18