analyze the graphed function to find the local minimum and the local maximum for the given function. which…

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.

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.

Answer

Explanation:

Step1: Analyze interval [1, 3]

The function has a local minimum at approximately (0.6, - 8) within [1, 3], not 0. So the statement "Over the interval [1, 3], the local minimum is 0" is false.

Step2: Analyze interval [2, 4]

The local minimum in the interval [2, 4] occurs at (3.4, - 8), so the statement "Over the interval [2, 4], the local minimum is - 8" is true.

Step3: Analyze interval [3, 5]

The local minimum in the interval [3, 5] occurs at (3.4, - 8), so the statement "Over the interval [3, 5], the local minimum is - 8" is true.

Step4: Analyze interval [1, 4]

The local maximum in the interval [1, 4] occurs at (2, 0), so the statement "Over the interval [1, 4], the local maximum is 0" is true.

Step5: Analyze interval [3, 5]

The local maximum in the interval [3, 5] is not 0. The function is increasing in part of this interval after the local - minimum at (3.4, - 8), so the statement "Over the interval [3, 5], the local maximum is 0" is false.

Answer:

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.