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 values at which f has a local minimum: all local minimum values of f:

Explanation:

Step1: Recall the definition of local minimum

A local minimum of a function \(y = f(x)\) is a point where the function changes from decreasing to increasing. On the graph, it is a "valley" point.

Step2: Identify the \(x -\)value (local minimum location)

Looking at the graph, the \(x -\)coordinate of the local - minimum point is \(x=-1\).

Step3: Identify the \(y -\)value (local minimum value)

The \(y -\)coordinate of the local - minimum point is \(y = 1\).

Answer:

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