Calculate the average rate of change for each function over the given interval. f(x) = ∛x for 5 ≤ x ≤ 9

What is the average rate of change of the function g(t) over the interval from t = a to t = b? How is it related to a secant line?

If the average rate of change of a function over [a, b] is zero, this means that the function has not changed over [a, b], right?

Find the average rate of change of the function over the given interval. Compare this average rate of change with the instantaneous rates of change at the endpoints of the interval.

f(t) = 4t + 5, [1,2]

In Neurospora, the mutant stp exhibits erratic stop-and start growth. The mutant site is known to be in the mtDNA. If an stp strain is used as the female parent in a cross with a normal strain acting as the male, what type of progeny can be expected? What about the progeny from the reciprocal cross?

Using Table 2.3, find the average rate of change in the world's population, P, between 1975 and 2010. Give units.

$$\begin{matrix} \text{Year} & \text{1975} & \text{1980} & \text{1985} & \text{1990} & \text{1995} & \text{2000} & \text{2005} & \text{2010}\\ \text{Population} & \text{4.08} & \text{4.45} & \text{4.84} & \text{5.27} & \text{5.68} & \text{6.07} & \text{6.45} & \text{6.89}\\ \end{matrix}$$

Calculate the average rate of change of the given function f over the intervals [a, a+h] where h=1, 0.1, 0.01, 0.001, and 0.0001. (Technology is recommended for the cases h=0.01, 0.001, and 0.0001) $f(x)=\frac{2}{x}$; a=1

Find the average rate of change of the function over the given interval or intervals. $f(x)=x^{3}+1$ a. [2, 3] b. [-1,1]

Calculate the average rate of change of the given function over the given interval. Where appropriate, specify the units of measurement. $f(x)=x^{2}-3$; [1, 3]

Calculate the average rate of change for each function over the given interval. g(x) = ∛x + 2 for -4 ≤ x ≤ 0

Which of the following statements is not true of firms in perfect competition? a. All producers charge the same price. b. All producers make the same product. c. Each firm tries to sell more by reducing its price. d. There are no barriers to entry.

Compare the average rate of change of the function over the given interval with the instantaneous rates of change at the endpoints of the interval. $g(x)=x^2+e^x,[0,1]$ 98, $h(x)=x^3-2 e^x, \quad[-1,0]$

In Exercises, compute the average rate of change of the function on the given interval. In Exercises, simplify your answer as much as possible.

f(x)=3 / x$on$[a, b]$

Solve the inequality. Graph the solution set on a number line: 6x + 14 ≥ 20