To determine the intervals during which the particle is moving to the left, we analyze the graph of $x(t)$. The particle moves left when its velocity, $x'(t)$, is negative. The velocity corresponds to the slope of the graph $x(t)$.

From the graph:

1. The slope is negative in the following intervals:
   • From $t = 4$ to $t = 6$ (descending from a local maximum).
   • From $t = 9$ to $t = 14$ (descending from a local maximum to a local minimum).

Answer:

The particle is moving to the left during the intervals: $(4, 6) \text{ and } (9, 14).$

Would you like a more detailed explanation or have any questions?
Here are some related questions to explore:

1. How do we mathematically identify intervals of increasing or decreasing behavior for a function?
2. What is the role of inflection points in analyzing motion along a curve?
3. How can we determine intervals of acceleration or deceleration for the particle?
4. Can we derive the velocity and acceleration graph from this position graph?
5. How would the result change if the graph included more complex features like vertical tangents?

Tip: Always check the graph's slope carefully to interpret velocity changes correctly!