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.

Step2: Identify local - minimum points on the graph

Looking at the graph, we can see that the function has local minima at the points where the graph changes from decreasing to increasing.

Step3: Determine local - minimum values

The \(y\) - values of the local minima are the local - minimum values of the function. The local - minimum values occur at \(y=-2\) and \(y = - 1\).

Step4: Determine \(x\) - values of local minima

The \(x\) - values at which the local minima occur are \(x=-0.5\) and \(x = 3\).

Answer:

All local minimum values of \(f\): \(-2,-1\)
All values at which \(f\) has a local minimum: \(-0.5,3\)