Originally Posted by

**CaptainBlack** Because these functions are both piecewise differentiable all we need to

show is that:

lim_{x->1-} f(x) = lim_{x->1+} f(x),

and that:

lim_{x->1-} f'(x) = lim_{x->1+} f'(x),

If both of these hold then the function is differentiable at x=1, otherwise they

are not.

For a) lim_{x->1-} f(x) = 1, lim_{x->1+} f(x) = 1, and lim_{x->1-} f'(x) = 3,

lim_{x->1+} f'(x) = 3, so f is differentiable at x=1.

For b) lim_{x->1-} f(x) = 3, lim_{x->1+} f(x) = 1, so f is not differentiable

at x=1.

RonL