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 local - minimum definition

A local minimum of a function occurs at a point where the function value is less than or equal to the values of the function at nearby points. On a graph, it is a "valley" point.

Step2: Identify x - values of local minima

Looking at the graph of \(y = f(x)\), we can see that the function has local minima at \(x = 0\) and \(x = 3\).

Step3: Identify local - minimum values

The \(y\) - values of the local minima are the \(y\) - coordinates of the points \((0,- 2)\) and \((3,-2)\). So the local - minimum value is \(-2\).

Answer:

All values at which \(f\) has a local minimum: \(0,3\)
All local minimum values of \(f\): \(-2\)