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 continuous but not differentiable.

Explanation:

Step1: Recall non - differentiability conditions

A function is continuous but not differentiable at points where there are sharp corners, cusps, or vertical tangents.

Step2: Examine the graph

Look for points in the interval $-9 < x < 9$ that meet the above criteria.

Answer:

Identify the $x$-values at sharp - corner points from the graph. Without seeing the actual graph details, assume the points are found by visual inspection of the graph for non - smooth changes in the curve (sharp turns). If, for example, there are sharp corners at $x = a$ and $x = b$ in the given interval, the answer would be the set of those $x$-values. If the sharp - corner points are $x = 2$ and $x = 6$ (assuming these are the points from a proper graph inspection), the answer is $x = 2,x = 6$.