Continuity And Differentiability

We are given a piecewise function:

Step 1: Check continuity at
Left-hand limit:
Right-hand limit:
Since both limits and , function is continuous at .

Step 2: Check differentiability at
Left-hand derivative:
Right-hand derivative:
Since left-hand and right-hand derivatives are not equal, function is not differentiable at .

Correct answer: (B) Continuous but not differentiable.