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The position of a moving car at time t is given by f(t) = at² + bt + c, t > 0, where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t₁, t₂] is attained at the point:
- a(t₂ − t₁) + b
- (t₁ + t₂)/2
- 2a(t₁ + t₂) + b
- (t₂ − t₁)/2
Correct answer: (t₁ + t₂)/2
Solution
The average speed of a car over a time interval is calculated by taking the change in position divided by the change in time. The average speed is best represented by the midpoint of the interval, (t₁ + t₂)/2, as it reflects the average value of the function over that interval.
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