Question

which interval for the graphed function contains the local minimum?
-1,1
1,2
-3,-1
-5,-3

Explanation:

Step1: Recall the definition of local minimum

A local minimum of a function is a point where the function changes from decreasing to increasing.

Step2: Analyze each interval

• For the interval \([-1,1]\): The function is decreasing then increasing but the local minimum is not in this interval.
• For the interval \([1,2]\): The function is decreasing.
• For the interval \([-3,-1]\): The function changes from decreasing to increasing.
• For the interval \([-5,-3]\): The function is increasing.

Answer:

\([-3,-1]\)