Question

Find the average rate of change of f(x) = 2x^2+6

Answer 1

Given:

$f(x)=2 x^{2}+6$

To find:

The average rate of change.

Solution:

Average rate of change formula:

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

(a) Average rate of change from 2 to 4:

Substitute x = 4 and x = 2 in f(x).

$\frac{f(4)-f(2)}{4-2}=\frac{(2(4)^2+6)-(2(2)^2+6)}{4-2}$

                  $=\frac{38-14}{2}$

                  = 12

Average rate of change from 2 to 4 is 12.

(b) Average rate of change from 1 to 3:

Substitute x = 3 and x = 1 in f(x).

$\frac{f(3)-f(1)}{3-1}=\frac{(2(3)^2+6)-(2(1)^2+6)}{3-1}$

                   $=\frac{24-8}{2}$

                   = 8

Average rate of change from 2 to 4 is 8.

(c) Average rate of change from -2 to 1:

Substitute x = 1 and x = -2 in f(x).

$\frac{f(1)-f(-2)}{1-(-2)}=\frac{(2(1)^2+6)-(2(-2)^2+6)}{1+2}$

                      $=\frac{8-14}{3}$

                       = -2

Average rate of change from 2 to 4 is -2.