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 maximum at $x = 2$ with value $y = 0$. There is no local minimum in the open - interval $(1,3)$. At the endpoints, we consider the behavior. The statement "Over the interval [1, 3], the local minimum is 0" is false as 0 is a local maximum in this interval.

Step2: Analyze interval [2, 4]

The function has a local minimum at approximately $x=3.4$ with $y = - 8$. So, the statement "Over the interval [2, 4], the local minimum is - 8" is true.

Step3: Analyze interval [3, 5]

The function has a local minimum at approximately $x = 3.4$ with $y=-8$. So, the statement "Over the interval [3, 5], the local minimum is - 8" is true.

Step4: Analyze interval [1, 4]

The function has a local maximum at $x = 2$ with $y = 0$. So, the statement "Over the interval [1, 4], the local maximum is 0" is true.

Step5: Analyze interval [3, 5]

The local minimum in [3, 5] is - 8, not a local maximum of 0. 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.