Question

Find the average rate of change of f(x) = 4x2 - 3 from 3 to 6.The average rate of change of f(x) = 4x² - 3 from 3 to 6 is(Simplify your answer.)

Answer 1

36

Given the function:

f(x) = 4x² - 3

To find the average rate of change of the function from 3 to 6, we have:

`Averagerate=(\Delta y)/(\Delta x)`

Thus, we have:

`\frac{f(6)-f(3)}{x2\text{ - x1}}`

where,

x2 = 6

x1 = 3

For f(6):

f(6) = 4(6)² - 3 = 144 - 3 = 141

For f(3):

f(3) = 4(3)² - 3 = 36 - 3 = 33

`\begin{gathered} \frac{141\text{ - 33}}{6\text{ - 3}} \\ \\ =\text{ }(108)/(3)\text{ = }36 \end{gathered}`

Therefore, the average rate of change of f(x) = 4x² - 3 from 3 to 6 is 36.