Question

select all the points at which the graph above is not differentiable-4-3-2-101234

Explanation:

A function is not differentiable at a point if:

1. There is a sharp corner (cusp) in the graph, as the left and right derivatives do not match.
2. There is a discontinuity (jump, hole, or break), since continuity is required for differentiability.

• At $x=-1$: The graph has a sharp corner, so it is not differentiable here.
• At $x=2$: There is a discontinuity (a hole and a filled point at different $y$-values), so the function is not differentiable here.

All other listed points have smooth, continuous graph segments with well-defined slopes.

Answer:

$\boldsymbol{\square -1}$
$\boldsymbol{\square 2}$