Average Rate Of Change Of A Function
Bayani Gaba-gaba
How fast is something changing? Over a stretch of a journey, the average speed answers that question, and the same idea works for any function. The average rate of change measures how much the output changes for each unit of input across an interval, capturing the overall trend between two points.
In this lesson you will calculate and interpret the average rate of change of a function over a specified interval. You will see that it is exactly the slope of the straight line joining the two endpoints, and learn to read what that number tells you about the situation.
Manufura
- Calculate and interpret the average rate of change of a function over a specified interval.
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- The average rate of change of f over [a, b] is: A. f(b) + f(a) B. (f(b) - f(a))/(b - a) C. f(b) * f(a) D. (b - a)/(f(b) - f(a)) Answer: B
- For f(x) = x^2, the average rate of change from x = 1 to x = 4 is: A. 3 B. 5 C. 15 D. 17 Answer: B
- A car goes from 100 km to 280 km between t = 2 and t = 5 hours. The average rate of change is: A. 36 km/h B. 60 km/h C. 90 km/h D. 180 km/h Answer: B
- A negative average rate of change means the function is, overall: A. increasing B. decreasing C. constant D. undefined Answer: B
- The average rate of change equals the slope of the line joining: A. the origin and (b, f(b)) B. the two endpoints (a, f(a)) and (b, f(b)) C. any two points D. the maximum and minimum Answer: B
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
Littattafan da ake ba da shawarar karantawa
Ƙarin koyo daga tushe na buɗe
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Sashen littafi
Rates of Change and Behavior of Graphs
Find the average rate of change of a function.
"Algebra and Trigonometry: Rates of Change and Behavior of Graphs" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/3-3-rates-of-change-and-behavior-of-graphs. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
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