Question

Find the average rate of change of f(x) with respect to x on the interval. $f(x)=x^2-4 ; [-4,3]$

Answer 1

Answer:

The average rate of function of f on the given interval is -1.

Step-by-step explanation:

Recall that the average rate of change is simply the slope of the function between two points.

We are given the function:

$f(x)=x^2-4$

And we want to find its average rate of change on the interval [-4, 3].

Evaluate the two endpoints:

$\displaystyle \begin{aligned} f(-4) & = (-4)^2 - 4 \\ \\ & = 16 - 4 \\ \\ & = 12\end{aligned}$

Likewise:
$\displaystyle \begin{aligned} f(3) & = (3)^2 - 4 \\ \\ & = 9 - 4 \\ \\ & = 5\end{aligned}$

Recall that slope is given by:

$\displaystyle m = \frac{\Delta y}{\Delta x}$

Hence, the average rate of change is:
$\displaystyle\begin{aligned} \text{Avg Rate of Change} & = \frac{(5)-(12)}{(3)-(-4)} \\ \\ &= \frac{-7}{7} \\ \\ & = -1\end{aligned}$

In conclusion, the average rate of function of the given function on the given interval is -