https://file.aiquickdraw.com/mathbot/file/1726506165354b7m5flqs.jpg

To determine where the function is not differentiable, we need to look for certain characteristics in the graph. A function is not differentiable at points where:

1. There is a **sharp corner** or **cusp**.
2. The function is **discontinuous** (a jump or a hole in the graph).
3. The **slope is vertical** (the tangent line has an infinite slope).

### From the graph:

- **At \(x = -4\)**: There is a sharp corner, which means the function is not differentiable at this point.
- **At \(x = -2\)**: There is a jump discontinuity (a gap in the function), so the function is not differentiable here.
- **At \(x = 0\)**: There is a hole in the graph, indicating a discontinuity, so the function is not differentiable at this point.
- **At \(x = 2\)**: There is a sharp corner, so the function is not differentiable at this point.

### Conclusion:
The function is not differentiable at **\(x = -4, -2, 0, 2\)**.

Would you like further explanation or details on why differentiability fails at these points? 

Here are 5 related questions to expand on this topic:

1. What is the formal definition of differentiability at a point?
2. How do continuous functions differ from differentiable functions?
3. Can a function be continuous but not differentiable at certain points?
4. What are the implications of having vertical tangents on differentiability?
5. How do limits play a role in determining differentiability?

**Tip:** If a function has a sharp corner or cusp, it's an indication that the left-hand and right-hand slopes do not match, hence it's not differentiable at that point.

Use the given graph of the function to find the x-values for which f is not differentiable.

Learn how to identify points where a function is not differentiable using a graph. This problem involves understanding sharp corners, discontinuities, and vertical tangents, providing a comprehensive analysis for high school students. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation