Question

question
consider the graph below. select all of the points at which the function has a local (not absolute) minimum over the interval -1.5,2.5.
select all that apply:
□ x = -1.1
□ x = 0
□ x = 1.1
□ x = 2

Explanation:

Step1: Recall local - minimum definition

A local minimum occurs at a point \(x = c\) if \(f(c)\) is less than or equal to \(f(x)\) for all \(x\) in some open interval containing \(c\).

Step2: Analyze the graph in the interval \([-1.5,2.5]\)

Inspect the graph for points where the function changes from decreasing to increasing.
In the given interval \([-1.5,2.5]\), at \(x = 0\), the function changes from decreasing to increasing, so it is a local - minimum. Also, at \(x = 2\), the function changes from decreasing to increasing, so it is a local - minimum.

Answer:

\(x = 0\)
\(x = 2\)