hw 7 - definition of the derivative section 2.2: problem 8 (1 point) use the given graph of the function to…

Explanation:

Step1: Recall non - differentiability conditions

A function is not differentiable at points of sharp corners, discontinuities.

Step2: Identify sharp corners

The graph has sharp corners. These are points where the left - hand and right - hand derivatives do not match.

Step3: Identify discontinuities

There are also open - circle and closed - circle type discontinuities.

Step4: Locate non - differentiable x - values

By observing the graph, we find the x - values.

Answer:

The function (f) is not differentiable at the (x) - values corresponding to the sharp corners and discontinuities. From the graph, these (x) - values (assuming the grid lines are at integer values and based on visual inspection) are (x=- 3, - 1,1,3) (answers may vary slightly depending on exact graph reading).