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, i.e., where the second - derivative changes sign. Graphically, it is where the graph changes from being concave up to concave down or vice - versa.

Step2: Analyze the graph

Looking at the given graph of (y = f(x)), we can see that the function changes concavity at (x = 0.5) and (x = 2.5). The function is concave up on some intervals and concave down on others, and these two points are the transition points.

Answer:

(x = 0.5) (smallest value) (x = 2.5) (largest value)