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 interval [-3, -2]

Check function values in [-3, -2]. The function value at x = - 2.2 is 0. Since the function does not go lower in this interval, the local - minimum is 0.

Step2: Analyze interval [-2, -1]

In [-2, -1], the function has a value of approximately 2.2 at x=-1.3, but it also has lower values near x = - 2. So 2.2 is not the local - minimum.

Step3: Analyze interval [-1, 0.5]

In [-1, 0.5], the function has a value of 1 at x = 0. But it has lower values near x=-1. So 1 is not the local - minimum.

Step4: Analyze interval [0.5, 2]

In [0.5, 2], the function value at x = 1 is 4. But it has lower values near x = 0.5. So 4 is not the local - minimum.

Answer:

Over the interval [-3, -2], the local minimum is 0.