the graph of the function f is shown above. of the following intervals, on which is f continuous but not…

Explanation:

Step1: Recall continuity and differentiability

A function is continuous if there are no breaks, jumps or holes. It is differentiable if the graph has a smooth non - sharp curve.

Step2: Analyze interval (0,1)

The graph is a straight - line segment in (0,1), so it is both continuous and differentiable.

Step3: Analyze interval (1,2)

The graph has a smooth curve in (1,2), so it is both continuous and differentiable.

Step4: Analyze interval (2,3)

There is a sharp corner at (x = 2). A function is not differentiable at a sharp corner. But the function is continuous in (2,3) as there are no breaks or jumps.

Step5: Analyze interval (3,4)

The graph is a smooth curve in (3,4), so it is both continuous and differentiable.

Answer:

C. (2,3)