Question

The average rate of change of a function f(x) = x2 between x = 3 and x = 9 is
average rate of change =

Answer 1

Answer:

12.

Step-by-step explanation:

Average rate of change = (value of the function when x = 9 - value when x=3)

/

(9 - 3)

= f(9) - f(3) / (9-3)

= (9^2 - 3^2) / (9-3)

= 72 / 6

=  12.

Answer 2

The average rate of change of a function is the rate at which the y-values change over the x-values.

The average rate of change of $f(x) = x^2$ between (3,9) is 12.

Given that:

$f(x) = x^2$

Where:

$x_1,x_2 = 3,9$

The average rate (m) of change is calculated as follows:

$m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

This gives:

$m = \frac{f(9) - f(3)}{9 -3}$

$m = \frac{f(9) - f(3)}{6}$

Calculate f(9) and f(3)

$f(x) = x^2$

$f(9) =9^2 = 81$

$f(3) =3^2 = 9$

So, we have:

$m = \frac{81 - 9}{6}$

$m = \frac{72}{6}$

$m =12$

Hence, the average rate of change is 12.

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