Advanced MathMediumAverage rate of change of a quadratic over an interval
Advanced Math practice question
The function f is defined by f(x) = x² + 1. What is the average rate of change of f from x = 1 to x = 4?
Answer: 5
Average rate of change = (f(4) − f(1))/(4 − 1) = (17 − 2)/3 = 15/3 = 5.
Common wrong answers
- If you answered 8
- 8 is the instantaneous rate at x = 4, not the average over the interval.
- If you answered 15
- 15 is f(4) − f(1), before dividing by the change in x.
- If you answered 17
- 17 is f(4) alone.
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