The graph of a cubic function $p(x)$ is shown in the first diagram below, for $0 \leq x \leq 4$, $x \in \mathbb{R}$ - Leaving Cert Mathematics - Question 6(c) - 2022

Given the graph of $p(x)$, the slope of the tangent at $x = 1$ indicates that $p'(1) = 0$. Therefore, we plot the point (1, 0).

At $x = 2$, the graph of $p(x)$ shows a local maximum; hence, $p'(2) = 1$. We plot the point (2, 1).

At $x = 3$, the slope of the tangent is also 0, indicating that $p'(3) = 0$. Thus, we plot the point (3, 0).

Finally, at $x = 4$, the graph of $p(x)$ indicates that $p'(4) = -3$. Hence, we plot the point (4, -3).

Now, connect the plotted points (0, -3), (1, 0), (2, 1), (3, 0), and (4, -3) with a smooth curve, ensuring the correct shape of the cubic function is represented. The graph should reflect the changes in slope as seen in the original cubic function's graph.