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 the definition of local minimum

A local minimum of a function \(y = f(x)\) is a point \((a,f(a))\) where \(f(a)\) is less than or equal to the values of \(f(x)\) in some open interval containing \(a\). Visually, it is a “valley” on the graph.

Step2: Identify the local minimum from the graph

Looking at the graph, we find the \(y -\)coordinate of the “valley” point. The \(y -\)value (local minimum value) at the local minimum point is \(0\) (since the point on the graph has \(y = 0\)), and the \(x -\)value (the value of \(x\) at which the local minimum occurs) is \(- 3\).

Answer:

All local minimum values of \(f\): \(0\)
All values at which \(f\) has a local minimum: \(-3\)