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^+} =

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

answer4 to the second power is 16

and 4 to the third power is 64,