The graph shows the estimated number of milligrams of a pain medication M in the

Question

The graph shows the estimated number of milligrams of a pain medication M in the bloodstream thours after a 1000-milligram dose of the drug has been given. Paln Iedkatlon In Bloodstreamm 1000 600 2-3-4-5-6 Hours (a) Estimate the one-hour interval over which the absolute value of the average rate of change is the greatest. (Enter your answer using interval notation.) (b) Over what interval is the average rate of change approximately equal to the rate of change at4? Explain your reasoning. O O O Both the instantaneous rate of change at t = 4 and the average rate of change on [2, 51 is about zero. Both the instantaneous rate of change at t = 4 and the average rate of change on [2, 5] is about negative two hundred Both the instantaneous rate of change at t = 4 and the average rate of change on [1, 6] is about two hundred Both the instantaneous rate of change at t = 4 and the average rate of change on [0, 6] is about two hundred. Both the instantaneous rate of change at t = 4 and the average rate of change on [1, 6] is about zero

Explanation / Answer

a) As the rate of change in the interval [5,6] is (600-0)/1=600 which is greatest over the entire one hour intervals.

So answer is [5,6].

b) as average rate of change in [2,5] = (600-600)/(5-2) = 0 (about 0), which is equal to the instantaneous change at 4 which is almost zero.

So the answer is first option.

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