What is $f'(1)$ for $f(x) = \begin{cases} x^{2} + 3x, & x \le 1 \\ 5x - 1, & x > 1 \end{cases}$?

Explanation

1. 01

   Values at 1: $1 + 3 = 4$ and $5 - 1 = 4$, so $f$ is continuous there.

2. 02

   Slopes: $2x + 3 = 5$ on the left and 5 on the right; they agree, so $f'(1) = 5$.