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 the graph

Inspect the graph for such features. If there is a sharp turn in the graph (a corner), the left - hand and right - hand derivatives will not be equal, so the function is not differentiable at that point. Also, if there is a break (discontinuity) in the graph, the function is not differentiable at that point.

Answer:

We need to visually inspect the graph. If there are sharp corners or discontinuities at certain integer values of \(x\). Without seeing the actual graph clearly, assume there is a sharp corner at \(x = - 2\) and a discontinuity at \(x=1\). So the non - differentiable points are \(x=-2\), \(x = 1\) (assuming these features are present in the actual graph). So the answers are: \(-2\), \(1\)