Question

select all the points at which the graph above is not differentiable

Explanation:

Step1: Recall non - differentiability conditions

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

Step2: Analyze sharp corners

At $x=- 2$, the graph has a sharp corner. The slope changes abruptly from positive to negative.

Step3: Analyze discontinuities

There is a jump discontinuity at $x = 1$. The function has a break in its graph at this point.

Step4: Analyze vertical tangents

There are no vertical tangents in the given graph.

Answer:

$x=-2$ and $x = 1$