Question

Find the average rate of change for the given function over the indicated values of x. If necessary, round your final answer to two decimal places.
f(x)=x^2+6x, where x goes from 5 to 7.

Answer 1

Answer:

The average rate of change of the function in this interval is of 18.

Step-by-step explanation:

The average rate of change of a function $f(x)$ in an interval from a to b is given by:

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

In this question:

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

Where x goes from 5 to 7.

This means that $b = 7, a = 5$. So

$f(7) = 7^2 + 6(7) = 49 + 42 = 91$

$f(5) = 5^2 + 6(5) = 25 + 30 = 55$

The rate of change is:

$A = \frac{f(7) - f(5)}{7 - 5} = \frac{91 - 55}{2} = 18$

The average rate of change of the function in this interval is of 18.