Question

which statement correctly identifies a local minimum of the graphed function?
over the interval -3, -2, the local minimum is 0.
over the interval -2, -1, the local minimum is 2.2.
over the interval -1, 0.5, the local minimum is 1.
over the interval 0.5, 2, the local minimum is 4.

Explanation:

Step1: Analyze the first option

Over the interval \([-3,-2]\), check the function values. The local minimum is not \(0\) as the function values in this interval are not \(0\).

Step2: Analyze the second option

Over the interval \([-2,-1]\), the local minimum is not \(2.2\). The function has lower values in this interval.

Step3: Analyze the third option

Over the interval \([-1,0.5]\), the local minimum is \(1\) (at \(x = 0\)).

Step4: Analyze the fourth option

Over the interval \([0.5,2]\), the local minimum is not \(4\). There are lower values in this interval.

Answer:

Over the interval \([-1,0.5]\), the local minimum is \(1\).