**Problem : **
For which values of
*x*
does the function
*f* (*x*)
, with graph shown below, fail
to be continuous? differentiable?

Figure %: Locate the Discontinuities

**Problem : **
For which values of
*x*
does the function
*f* (*x*)
with the following graph have
*f'*(*x*) = 0
?

Figure %: Locate the Points for which
*f'*(*x*) = 0

**Problem : **
Let
*f* (*x*) = *x*
^{1/3}
, a function defined on the entire real line. Is
*f*
differentiable at
*x* = 0
?

**Problem : **
Let
*f* (*x*) = sin(*x*)
. For which values of
*x*
is
*f'*(*x*) = 0
?