Question

here is a graph of the function f. use the graph to find the following. if there is more than one answer, separate them with commas. all local minimum values of f. all values at which f has a local minimum:

Explanation:

Step1: Recall local - minimum definition

A local minimum of a function \(y = f(x)\) is a point where the function value is less than or equal to the values of the function in a small neighborhood around that point. Visually, on a graph, it is a "valley" point.

Step2: Examine the graph

Looking at the given graph of the function \(f\), we search for the "valley" points. We can see that the function has local - minimum points at \(x=- 3\) and \(x = 2\).

Step3: Determine the local - minimum values

To find the local - minimum values, we look at the \(y\) - coordinates of these local - minimum points. When \(x=-3\), \(y = - 2\); when \(x = 2\), \(y=-2\).

Answer:

The local - minimum values of \(f\) are \(-2\). The values of \(x\) at which \(f\) has a local minimum are \(-3,2\).