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: Check interval [1, 3]

From the graph, in [1, 3], the function value at x = 2 is 0. There are no lower - valued points in this interval, but this is a local maximum, not a local minimum. So the statement "Over the interval [1, 3], the local minimum is 0" is false.

Step2: Check interval [2, 4]

In the interval [2, 4], the lowest - valued point is at (3.4, - 8). So the local minimum over the interval [2, 4] is - 8. This statement is true.

Step3: Check interval [3, 5]

In the interval [3, 5], the lowest - valued point is at (3.4, - 8). So the local minimum over the interval [3, 5] is - 8. This statement is true.

Step4: Check interval [1, 4]

In the interval [1, 4], the highest - valued point is at x = 2 with a y - value of 0. So the local maximum over the interval [1, 4] is 0. This statement is true.

Step5: Check interval [3, 5]

In the interval [3, 5], the local minimum is - 8 and the local maximum occurs at the endpoints or local peaks. The local maximum is not 0. This statement 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.