Question

What is the average rate of change in f(x) over the interval [4,13]?

Answer 1

By definition, the average rate of change of any function f(x) in any given closed interval [a,b] is:

$f_{average}=\frac{1}{b-a}\int_{a}^{b}f(x)dx$

So, applying that definition here, we see that here a=4 and b=13.

Therefore, the average rate of change in f(x) over the interval [4,13] will be depicted as:

$f_{average}=\frac{1}{13-4}\int_{4}^{13}f(x)dx=\frac{1}{9}\int_{4}^{13}f(x)dx$

Thus, $\frac{1}{9}\int_{4}^{13}f(x)dx=\frac{\int_{4}^{13}f(x)dx}{9}$ is the correct answer.

Answer 2

Thank you for asking this question. The options for this question are missing:

Here are the missing options:

a. 1/3

b.4/13

c. 11/13

d.11/8

Answer:

A = (f(b) - f(a)/(b-a)

a = 4

b = 13

f(a) = f(4) = 8

f(b) = f(13) = 11

A = (11-8)/(13-4)

A = 3/9

Now we will divide the numerator as well as denominator by 3

A = 1/3

So the answer for this would be option A: 1/3