Mathematics: In which of the following intervals is the average rate of change greater for f than for g

In which of the following intervals is the average

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05.01.2022

Option B

[3, 5]

Step-by-step explanation:

The function g(x) is a line of slope m = 4. Therefore, its rate of change is constant and equal to 4.

The rate of change of the function f(x) in the interval [x_1, x_2] is calculated with the following formula

$m =\frac{y_2-y_1}{x_2 - x_1}$

Note that the rate of change of the function increases as x increases.

For example

For [-1, 0]

$m =\frac{4-3.5}{0 - (-1)}$

$m =\frac{1}{2}$

$\frac{1}{2}$

For [0, 2]

$m =\frac{7-4}{2 - 0}$

$m =\frac{3}{2}$

$\frac{3}{2}$

For [1, 3]

$m =\frac{11-5}{3-1}$

m =3

For [3, 5]

$m =\frac{35-11}{5-3}$

m =12

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