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

MATH102 December 2015
Other MATH102 Exams

### Question 19 (e)

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 ${\displaystyle E(t)}$ 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 ${\displaystyle E'(t)=4-t+{\frac {1}{16}}t^{2}}$

(e) Sketch ${\displaystyle E(t)}$. Label any minima, maxima and/or inflection points. On the same axes, draw a line that shows when the average error rate is minimized.

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