According to the alternate form of the definition of the derivative, to compute f'(0), we need to compute the left-hand limit

Let 

$f(x)= \begin{cases} -4x^{2}+4x & \text{for } x < 0, \\ 7x^{2}-5 & \text{for } x \geqslant 0. \end{cases}$

According to the alternate form of the definition of the derivative, to compute $f'(0)$, we need to compute the left-hand limit
 

$\lim \limits _ {x \to 0^-}$ ?, which is ?,

and the right-hand limit

$\lim \limits _ {x \to 0^+}$ ?, which is ?.