Question

a) what is average rate of change of f(x) over the interval from x=5 to x=9? (table shows values of f(x). graph shows function of g(x).)

table:
x: 4, 5, 6, 7, 8, 9, 10
F(x): -8, -4, 8, 10, 11, 14 ,18


b) Find the average rate of change of g(x) over the interval from x = 0.25 to x= 1. (Write answer as a simplified fraction. Show work)

c) if g(x) represents the height of a ball that was throw. up into the air, interpret your answer from part b) in terms of the real-world it represents.

Answer 1

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

The average rate of change of a function over the interval $[a,b]$ is equal to $\frac{f(b)-f(a)}{b-a}$, hence:

$\frac{f(b)-f(a)}{b-a}\\\\\frac{f(9)-f(5)}{9-5}\\\\\frac{14-(-4)}{9-5}\\ \\\frac{14+4}{4}\\ \\\frac{18}{4}\\ \\\frac{9}{2}$

Therefore, the average rate of change of $f(x)$ over the interval $[5,9]$ is $\frac{9}{2}$.

Part B

Do the same thing as in Part A:

$\frac{f(b)-f(a)}{b-a}\\ \\\frac{f(1)-f(0.25)}{1-0.25}\\ \\\frac{2-5}{0.75}\\ \\\frac{-3}{0.75}\\ \\-4$

Therefore, the average rate of change of $g(x)$ over the interval $[0.25,1]$ is $-4$.

Part C

To interpret our answer from Part B in terms of the real world it represents, we say that between 0.25 seconds and 1 second, the ball falls at a rate of 4 feet per second (since our average rate of change is negative).

Answer 2

The average rates of change are:

• a) 4.5
• b) -4
• c) It means that in the interval, for each second that passes the height decreases by 4ft.

How to get the average rate of change?

For a function f(x), the average rate of change on the interval [a, b] is:

$r = \frac{f(b) - f(a)}{b -a}$

a) Here we have:

$r = \frac{F(9) - F(5)}{9 - 5} = \frac{14 - (-4)}{4} = 4.5$

b) Now we look at g(x) on the interval [0.25, 1]

Notice that g(0.25) = 5 and g(1) = 2

Then we have:

$r = \frac{2 - 5}{1 - 0.25} = -4$

c) That average rate of change means that, in average, in that interval in each second the height decreases by 4 ft.

If you want to learn more about average rates of change:

https://brainly.com/question/8728504

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