Science:Math Exam Resources/Courses/MATH102/December 2015/Question 19 (a)
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Question 19 (a) 

In deciding how long a resident’s shift in the emergency room should be, the Chief of Staff at Vancouver General Hospital would like to minimize the average rate at which errors are made. Let be the number of errors made by a resident from the start of a shift until t hours into the shift. The instantaneous rate of change of errors made is (a) During what interval of time is increasing? decreasing? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

If on , then is increasing on the interval. On the other hand, if on , then is decreasing on the interval. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. First, we find the derivative of ;
Then, by Hint, when , we have , so that is increasing. On the other hand, for , and hence is decreasing.
Therefore, is 