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The graph shows the function \( f \) plotted on the coordinate plane. To determine the points where \( f \) is continuous but not differentiable, we need to identify locations where there are sharp corners, cusps, or vertical tangents.

By examining the graph, we can see:

- There is a sharp corner at \( x = 1 \).
- There is another sharp corner at \( x = 4 \).

These points indicate where the function is continuous (there are no breaks in the graph) but the function's derivative does not exist due to the abrupt change in direction.

Therefore, the correct answer to the question regarding the values of \( x \) at which \( f \) is continuous but not differentiable is \( x = 1, 4 \).

Would you like further details or have any other questions about this topic? Here are some related questions:

1. How can you determine the differentiability of a function just by looking at its graph?
2. What is the definition of a differentiable function?
3. Can a function be differentiable at a point where it is not continuous?
4. How do derivatives relate to the slope of a tangent line on a graph?
5. What types of discontinuities might a function have?

**Tip:** When examining a graph to determine differentiability, look for points where there is a sudden change in the direction of the graph (corners or cusps) or where the slope would be undefined (vertical tangent lines).

Use the graph to find all values of x at which f is continuous but not differentiable.

Learn how to identify points of continuity where the function is not differentiable on a graph. This example focuses on sharp corners and explains the relationship between continuity and differentiability. Suitable for Grades 10-12.

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