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 occurs where the function changes from decreasing to increasing. By observing the graph, we can see such points.

Step2: Determine local - minimum values

The local - minimum values are the $y$ - coordinates of the local - minimum points. From the graph, the local - minimum values are $y=-3,y = - 5$.

Step3: Determine $x$ - values at local minima

The $x$ - values at which the local minima occur are the $x$ - coordinates of the local - minimum points. From the graph, these values are $x=-2,x = 4$.

Answer:

All local minimum values of $f$: $-3,-5$
All values at which $f$ has a local minimum: $-2,4$