#tex2html_wrap_inline2973#, we
obtain the following derivation:
#equation1795#
and
#equation1798#
which is not continuous. For a pictorial representation, see
Figure-(#tex2html_wrap_inline2975#).
On the issue of first and second derivatives continuity of the
function defined in equation (#tex2html_wrap_inline2977#), the first
derivative of equation (#tex2html_wrap_inline2979#) is clearly continuous as well
as that of equation (#tex2html_wrap_inline2981#).
About the second derivatives of equations (#tex2html_wrap_inline2983# and
#tex2html_wrap_inline2985#) we get the following:
#equation1801#
Therefore, as shown in Figure-(#tex2html_wrap_inline2987#), the function's graph
is broken at 0. Hence, #tex2html_wrap_inline2991# is not a continuous function.
#figure592#
Figure 3: A plot showing the #tex2html_wrap_inline2993# derivative (#tex2html_wrap_inline2995#) of #tex2html_wrap_inline2997#
at k=1, which is #tex2html_wrap_inline3001#.
#figure599#
Figure 4: A plot showing the #tex2html_wrap_inline3003# derivative (#tex2html_wrap_inline3005#) of
#tex2html_wrap_inline3007#, which is #tex2html_wrap_inline3009#.