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…

Explanation:

Step1: Recall continuity and differentiability conditions

A function is not continuous at a point if there is a break, jump or hole. A function is not differentiable at a point if it is not continuous there, or if there is a sharp - corner or cusp.

Step2: Examine the graph in the interval (0,5)

Looking at the graph in the interval (0,5), we see a hole in the graph.

Answer:

There is a hole in the graph in the interval (0,5). If the x - value of the hole is (x = a) (from the graph, assume the x - value of the hole is (x = 1) for example, you need to read it precisely from the graph), then the function (f) is not continuous and not differentiable at that (x) - value. So for part a, if the x - value of the non - continuity is (x = c) (read from the graph), the answer is (x = c). For part b, since non - continuity implies non - differentiability, the x - value(s) where (f) is not differentiable is/are the same (x) - value(s) as where it is not continuous in the interval (0,5). So if the non - continuity point is (x = k) (from the graph), the answer for both a and b is (x=k) (replace (k) with the actual x - value from the graph).