Question

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

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)