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Maximum traffic flow over average speed

High school · ●●●○○ 50 pts

On a certain road section, the traffic flow yy (in thousands of vehicles per hour) and the average speed vv (in km/h) of vehicles satisfy y=670(v−5)v2−8v+915y=\frac{670(v-5)}{v^2-8v+915} for v>5v>5. Find the average speed vv at which the traffic flow is largest, and the maximum traffic flow. Round the maximum traffic flow to one decimal place.

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optimizationAM-GM inequalityrational functions