Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.

Explanation

To determine if there exists a function that is continuous everywhere but not differentiable at exactly two points, we can construct such a function and verify its properties.

### Step-by-Step Solution:

1. **Define the Function**:
Let's define a piecewise function \( f(x) \):
\[
f(x) =
...