Let
f(x)= \left\lbrace \begin{array}{ll} -7 x^2 + 7 x & \mbox{for }x< 0\ 5 x^2 - 5 & \mbox{for }x\ge 0\ \end{array}\right.
according to the definition of derivative, to compute f'(0), we need to compute the left-hand limit
\lim_{x\to 0^-} =
and the right-hand limit
\lim_{x\to 0^+} =