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: Identify local minimum points

Local minimum points are where the function changes from decreasing to increasing. From the graph, we can see two such points.

Step2: Determine local - minimum values

For the first local - minimum point near \(x=-3\), the \(y\) - value is \(1\). For the second local - minimum point near \(x = 3.5\), the \(y\) - value is \(-2\). So the local minimum values of \(f\) are \(1,-2\).

Step3: Determine \(x\) - values of local minimum points

The \(x\) - value of the first local - minimum point is \(-3\) and the \(x\) - value of the second local - minimum point is \(3.5\). So the values at which \(f\) has a local minimum are \(-3,3.5\).

Answer:

All local minimum values of \(f\): \(1,-2\)
All values at which \(f\) has a local minimum: \(-3,3.5\)