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 interval [-3, -2]

There is no point in the graph within the interval [-3, -2] with a y - value of 0, so this is incorrect.

Step2: Analyze the interval [-2, -1]

The point (-1.3, 2.2) is in the interval [-2, -1] and it is a local minimum for this interval as the function values around it in this interval are higher.

Step3: Analyze the interval [-1, 0.5]

The local minimum in the interval [-1, 0.5] is at the point (0, 1), not 1 (1 is the y - value, but the statement is not correctly worded in this option).

Step4: Analyze the interval [0.5, 2]

The local minimum in the interval [0.5, 2] is not 4 as there is no such minimum value in this interval.

Answer:

Over the interval [-2, -1], the local minimum is 2.2.