here is a graph of the function f. use the graph to find the following. if there is more than one answer…

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:

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:

Answer

Explanation:

Step1: Recall local - minimum definition

A local minimum of a function (y = f(x)) occurs at a point (x = c) if (f(c)) is less than or equal to the values of (f(x)) for (x) in some open interval containing (c). On the graph, these are the "valleys".

Step2: Identify (x) - values of local minima

Looking at the graph, the function (f(x)) has local minima at (x=-1) and (x = 3).

Step3: Identify the local - minimum values

To find the local - minimum values, we look at the (y) - coordinates of the points where the local minima occur. When (x=-1), (y = - 2) and when (x = 3), (y=-1).

Answer:

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