select all the points at which the graph above is not differentiable\n□ -4\n□ -3\n■ -2\n□ -1\n□ 0\n□ 1\n■…

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

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

Answer

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 at (x=-2)

At (x = - 2), there is a sharp corner. The slope of the function changes abruptly at this point, so the left - hand derivative and the right - hand derivative are not equal. Thus, the function is not differentiable at (x=-2).

Step3: Analyze the graph at (x = 2)

At (x = 2), there is a discontinuity (a hole in the graph). A function must be continuous at a point to be differentiable there. Since it is not continuous at (x = 2), it is not differentiable at (x = 2).

Step4: Analyze other points

At (x=-4,-3,-1,0,1,3,4), the graph is smooth and has no sharp corners, cusps, vertical tangents, or discontinuities. So the function is differentiable at these points.

Answer:

-2, 2