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 the interval [1,3]

For the interval [1,3], the lowest - point (local minimum) is not 0. The function has a local maximum at \(x = 2\) (value \(y=0\)) in this interval.

Step2: Analyze the interval [2,4]

For the interval [2,4], the lowest - point (local minimum) occurs at \(x = 3.4\) (value \(y=-8\)).

Step3: Analyze the interval [3,5]

For the interval [3,5], the lowest - point (local minimum) is at \(x = 3.4\) (value \(y = - 8\)).

Step4: Analyze the interval [1,4]

For the interval [1,4], the highest - point (local maximum) occurs at \(x = 2\) (value \(y = 0\)).

Step5: Analyze the interval [3,5]

For the interval [3,5], the highest - point (local maximum) occurs at \(x = 4\) (value \(y = 0\)).

Answer:

B. Over the interval [2,4], the local minimum is - 8; D. Over the interval [1,4], the local maximum is 0; E. Over the interval [3,5], the local maximum is 0.