Let
$f(x) = \begin{cases} 5x - 3x^2 & \text{for } x < 0 \\ 8x^2 + 5x & \text{for } x \ge 0 \end{cases}$
According to the definition of the 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^+} $
We conclude that $f'(0)$ is
Note: If a limit or derivative is undefined, enter 'undefined' as your answer.
