the following is the graph of a function (f = f(x)). find the (x)-value of the inflection points of (f(x))…

Explanation:

Step1: Recall inflection - point definition

Inflection points are where the concavity of the function changes. On a graph, this is where the curve changes from being concave - up to concave - down or vice - versa.

Step2: Identify inflection points on the graph

By observing the given graph of (y = f(x)), we look for the (x) - values where the curvature changes.

Step3: Determine the smallest and largest (x) - values

From the graph, we can see that the inflection points occur at (x = 0.5), (x = 1.5), (x = 2.5). The smallest of these values is (x = 0.5) and the largest is (x = 2.5).

Answer:

Smallest value: (0.5) Largest value: (2.5)