Question

analyze the graphed function to find the local minimum and the local maximum for the given function. which statements about the local maximums and minimums for the given function are true? choose three options. over the interval 1, 3, the local minimum is 0. over the interval 2, 4, the local minimum is -8. over the interval 3, 5, the local minimum is -8. over the interval 1, 4, the local maximum is 0. over the interval 3, 5, the local maximum is 0.

Explanation:

Step1: Analyze interval [1, 3]

The function values in [1, 3] have a minimum at the point (2, 0). So the local - minimum over [1, 3] is 0.

Step2: Analyze interval [2, 4]

The function values in [2, 4] have a minimum at the point (3.4, - 8). So the local - minimum over [2, 4] is - 8.

Step3: Analyze interval [3, 5]

The function values in [3, 5] have a minimum at the point (3.4, - 8). So the local - minimum over [3, 5] is - 8.

Step4: Analyze interval [1, 4]

The function values in [1, 4] have a maximum at the point (2, 0). So the local - maximum over [1, 4] is 0.

Step5: Analyze interval [3, 5]

The function values in [3, 5] have a maximum at the point (5, 3). So the local - maximum over [3, 5] is not 0.

Answer:

Over the interval [1, 3], the local minimum is 0; Over the interval [2, 4], the local minimum is - 8; Over the interval [1, 4], the local maximum is 0.