Chapter 3: Derivatives - Section 3.2 - The Derivative as a Function - Exercises 3.2 - Page 117: 46

a. all points except $x=-1, 0, 2$ b. $(-1,0)$ c. $x=0, 2$

a. Examine the graph given by the exercise. We can find that all the points in the interval of the function are differentiable except at $x=1, 0$ (derivatives of opposite signs), and at the point at $x=2$ because the function is not continuous at this point (removable discontinuity). b. Examine the graph given by the exercise. We can find that one point at $(-1,0)$ in the interval of the function is continuous but not differentiable. This point is continuous because the left and right limits are equal to the function value at this point. c. Examine the graph given by the exercise. We can find that two points at $x=0, 2$ in the interval of the function are neither continuous nor differentiable. The graph is not continuous at $x=0$ because of the gap (also see part-a).