Question

use the graph of the function $f(x)$ shown below in order to determine all values of $x$ in the interval $-9 < x < 9$ where the function is not differentiable.

Explanation:

Step1: Recall non - differentiability conditions

A function is not differentiable at points of discontinuity, sharp corners, and vertical tangents.

Step2: Identify discontinuities

From the graph, there are jump - discontinuities at \(x=- 6\) and \(x = 1\).

Step3: Identify sharp corners

There are no sharp corners in the given graph.

Step4: Identify vertical tangents

There is a vertical tangent at \(x = 4\).

Answer:

\(x=-6,1,4\)