Hence
the first derivative at the origin exists because f¢(0)=0 on both the
left and the right of the origin.
The second derivative:
f¢¢(x)
= 0 for x £ 0
= 4 for x > 0.
Hence
the second derivative does not exist at the origin because on the
left the limiting value of f¢¢(x) as x® 0 is 0 whereas on
the right the limiting value of f¢¢(x) as x® 0 is 4.
).GIF)