A hillside profile is drawn with the horizontal distance x and the height y both in metres (m)…

Step 1. The quotient. $f(3) = 9 - 12 = -3$. $f(3 + h) = (3 + h)^2 - 4(3 + h) = -3 + 2h + h^2$. So $\dfrac{f(3 + h) - f(3)}{h} = \dfrac{2h + h^2}{h} = 2 + h$.

Step 2. The limit. As $h \to 0$, $2 + h \to 2$. So the slope at $x = 3$ m is $2$.

Step 3. The general derivative. $f'(x) = 2x - 4$. At $x = 3$ this is $2$, which agrees.

Step 4. The level point. $2x - 4 = 0$ gives $x = 2\ \text{m}$.