Question

select all the points at which the graph above is not differentiable
-4
-3
-2
-1
0
1
2
3
4

Explanation:

Step1: Recall non - differentiability conditions

A function is not differentiable at a point if there is a sharp corner, a cusp, a vertical tangent, or a discontinuity at that point.

Step2: Analyze sharp corners

At \(x=-3\), the graph has a sharp corner. The slope of the left - hand side of the graph and the right - hand side of the graph at \(x = - 3\) are different, so the function is not differentiable at \(x=-3\).

Step3: Analyze discontinuity

At \(x = 1\), there is a hole (removable discontinuity) in the graph. Since the function is not continuous at \(x = 1\), it is not differentiable at \(x = 1\).

Answer:

-3, 1