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 with sharp corners, vertical tangents, or discontinuities.

Step2: Examine sharp corners

At $x=-4$, there is a sharp corner. The left - hand and right - hand derivatives are different.

Step3: Examine vertical tangents

At $x = 7$, the function has a vertical tangent. The slope approaches infinity.

Answer:

$x=-4,x = 7$