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Does there exist a function which is con...

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

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To determine if there exists a function that is continuous everywhere but not differentiable at exactly two points, we can construct a specific example using the modulus function. ### Step-by-Step Solution: 1. **Understanding the Problem**: We need to find a function that is continuous at all points in its domain but fails to be differentiable at exactly two points. 2. **Choosing a Function**: A suitable function for this requirement is \( f(x) = |x + 1| + |x - 2| \). This function is composed of two modulus functions. ...
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