Question

graphs using local maximum and local minimum values use the graph to find the local minimum and the local maximum for the given function. hover over (or tap) a point to see its coordinates. over the interval -3, 0, the local minimum is over the interval 0, 3, the local maximum is over the interval 0, 3, the local minimum is

Explanation:

Step1: Analyze interval [-3, 0]

Look at the graph on [-3, 0]. The lowest point (local minimum) has y - value - 16.18? Wait, no, the point at x=-2 (in [-3,0]) has y=-16? Wait, the options have -16.18? Wait, maybe calculation. Wait, the interval [-3,0]: the local minimum is at the bottom of the left curve. From the graph, the coordinates: when x is between -3 and 0, the minimum y is -16.18? Wait, the options include -16.18. Wait, maybe I misread. Wait, the first blank: over [-3,0], local minimum. The graph on [-3,0] has a minimum at ( - 2, - 16) maybe, but the option is -16.18. So that's the local minimum.

Step2: Analyze interval [0, 3] local maximum

On [0,3], the local maximum is at x=1, y=4? Wait, no, the options have 3.75? Wait, maybe the point is (1, 3.75)? Wait, the graph: at x=1, the peak. So local maximum over [0,3] is 3.75.

Step3: Analyze interval [0, 3] local minimum

On [0,3], the local minimum is at x=2, y=-3? Wait, the option is -3. So that's the local minimum.

Answer:

Over the interval \([-3, 0]\), the local minimum is \(-16.18\).
Over the interval \([0, 3]\), the local maximum is \(3.75\).
Over the interval \([0, 3]\), the local minimum is \(-3\).