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函数的平均变化率
函数在区间上的平均变化率是什么意思？
1. Introduction
Introduction
2. Defining and interpreting the average rate of change of a function
Defining and interpreting the average rate of change of a function
3. How average rate of change indicates function trends
How average rate of change indicates function trends
4. Average rate of change on a falling interval
For s(t) = 64 - 16(t-1)^2 in feet, compute the average rate of change on [1.5, 2.5]. Give feet per second, including the sign.
5. Kent County's average growth rate
Kent County's population went from 500,631 in 1990 to 602,622 in 2010. What was its average rate of change in people per year over that interval? Round to the nearest whole person per year.
6. Interpreting Ottawa County's average rate
Ottawa County grew from 187,768 in 1990 to 263,801 in 2010. Which sentence correctly reads this average rate of change?
7. Predicting Ottawa's 2018 population
Ottawa County had 263,801 people in 2010 and grew at about 2,548.8 people per year over 2000-2010. Using that rate, predict its 2018 population, rounded to the nearest whole person.
8. Average rates on the quadratic q
For q(x) = 4 - (x-2)^2 the average rates on [0,1], [1,2], [2,3], [3,4] are 3, 1, -1, -3. Which statement is correct?
9. Average rates on the exponential-type h
For h(t) = 3 - 2(0.5)^t the average rates on [-1,1], [1,3], [3,5] are 1.5, 0.375, 0.094. What do they show about h on [-1,5]?
10. A positive average rate implies increase throughout
If a function's average rate of change over an interval is positive, then the function is increasing at every point of that interval.
11. Sketching a function from its average rate
Which of these sets of conditions can be satisfied by some function, according to the average-rate constraints?
12. Constant average rate everywhere
Which family of functions has the same average rate of change on every interval?