From the graph provided, let's identify the points where the function $f(x)$ is not differentiable. A function is not differentiable at points where:

1. The graph has sharp corners or cusps.
2. There are discontinuities (gaps or jumps).
3. The slope becomes vertical (though this case doesn't seem relevant here).

Observations from the Graph:

1. Leftmost non-differentiable point:

   • At $x = -5$, the graph has a sharp corner (cusp-like feature), so $f(x)$ is not differentiable here.

2. Rightmost non-differentiable point:

   • At $x = 2$, there is a jump discontinuity (filled circle at $(-4, 2)$ and open circle at $(-7, 2)$), so $f(x)$ is not differentiable here.

Answers:

• Leftmost $x$: $x = -5$
• Rightmost $x$: $x = 2$

Would you like further explanation or details on how differentiability works?

Related Questions to Explore:

1. Why is differentiability not defined at sharp corners or cusps?
2. How does the definition of continuity relate to differentiability?
3. Can a function be continuous but not differentiable? Provide examples.
4. What are the conditions for a function to be differentiable at a point?
5. How do vertical tangents affect differentiability?

Tip:

Always analyze the graph for both local behavior (e.g., sharp corners) and global properties (e.g., discontinuities) when checking differentiability.