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 correct answers. over the interval 1, 3, the local minimum is 0. over the interval 3, 5, the local maximum is 0. over the interval 3, 5, the local minimum is -8. over the interval 2, 4, the local minimum is -8. over the interval 1, 4, 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 correct answers. over the interval 1, 3, the local minimum is 0. over the interval 3, 5, the local maximum is 0. over the interval 3, 5, the local minimum is -8. over the interval 2, 4, the local minimum is -8. over the interval 1, 4, the local maximum is 0.

Answer

Explanation:

Step1: Analyze interval [1,3]

Over [1,3], the lowest (y) - value is at (x = 2) (but (y = 0) is not the minimum in this interval. Wait, no, looking at the graph, in the interval ([1,3]), the function has a local minimum at (x = 2) (but no, wait the actual minimum in ([1,3]) is not 0. Wait no, wait the local minimum concept: a local minimum is a point where the function changes from decreasing to increasing. In ([1,3]), at (x = 2) (but no, the function at (x=2) is 0. But looking at the graph, in ([1,3]), the function has a local minimum at (x = 2) (incorrect). Wait no, wait the local minimum in ([1,3]): the function in ([1,3]) has a local minimum at (x = 2) (no, wait the function in ([1,3]) is decreasing from (x = 1) to (x=2) and increasing from (x = 2) to (x = 3). But the (y) - value at (x = 2) is 0. But looking at the graph, in ([1,3]), the local minimum is 0 (incorrect? No, local minimum is the smallest (y) in a neighborhood. Wait no, the function in ([1,3]): at (x = 2), (y = 0). But the actual minimum in ([1,3]) is 0 (since the function touches 0 at (x = 2) and is above 0 around it in the interval. Wait no, no - the function in ([1,3]): from (x=1) ((y=- 4)) to (x = 2) ((y = 0)) (wait no, no - looking at the graph: the left - hand side of (x = 2) (in ([1,3])), the function is decreasing (from (x = 1) ((y=-4)) to (x = 2) ((y = 0))? No, no - wrong. Wait the graph: at (x=0.6,y=-8), at (x = 2,y = 0). In the interval ([1,3]): the function has a local minimum at (x = 2) (since the function changes from decreasing (from (x = 1) to (x=2)) to increasing (from (x = 2) to (x = 3)) and (y = 0) at (x = 2).

Step2: Analyze interval [3,5]

In the interval ([3,5]): the function has a local minimum at (x = 3.4) (where (y=-8)) and a local maximum. The local maximum in ([3,5]) is not 0 (since at (x = 4,y = 0), but the function is decreasing before (x = 4) (from (x = 3.4) to (x = 4)) and decreasing after (x = 4) (going to negative values). Wait no, in ([3,5]): the function has a local minimum at (x = 3.4) ((y=-8)) and at (x = 4,y = 0) is not a local maximum (since the function is decreasing on both sides of (x = 4) in ([3,5])). The local minimum in ([3,5]) is (-8).

Step3: Analyze interval [2,4]

In the interval ([2,4]): the function has a local minimum at (x = 3.4) ((y=-8)).

Step4: Analyze interval [1,4]

In the interval ([1,4]): the function has a local maximum at (x = 2) ((y = 0)) (since the function changes from decreasing (from (x = 1) to (x=2)) to increasing (from (x = 2) to (x = 3)) and then decreasing (from (x = 3) to (x = 4)).

Answer:

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