Question

use the graph of f in the figure to do the following. a. find the values of x in the interval (0,5) at which f is not continuous. b. find the values of x in the interval (0,5) at which f is not differentiable. a. in the interval (0,5), f is not continuous at x = (use a comma to separate answers as needed.)

Explanation:

Step1: Recall continuity condition

A function is not continuous at a point if there is a break, jump or hole in the graph at that point in the given interval $(0,5)$.

Step2: Examine the graph

Look for any such features in the interval $(0,5)$. If there is a hole, the function value is not well - defined at that $x$ - value; if there is a jump, the left - hand and right - hand limits are not equal.

Step3: Recall differentiability condition

A function is not differentiable at a point if it is not continuous at that point, or if there is a sharp corner (where the left - hand and right - hand derivatives are not equal) in the graph in the interval $(0,5)$.

Step4: Identify non - continuous points

From the graph, find the $x$ - values in $(0,5)$ where the function has breaks, jumps or holes.

Step5: Identify non - differentiable points

After finding non - continuous points (which are non - differentiable), also look for sharp corners in the continuous part of the graph in $(0,5)$.

Answer:

a. [List the $x$ - values in $(0,5)$ where the function is not continuous separated by commas]
b. [List the $x$ - values in $(0,5)$ where the function is not differentiable separated by commas]

(Note: Since the actual graph details are not clear enough to give exact numerical values, the above is a general step - by - step for answering the question. If you can provide more details about the graph features like exact locations of breaks, jumps, holes or sharp corners, a more specific answer can be given.)