Question

What is the average rate of change over the interval [1,4]Type the numerical value for your answer as a whole number, decimal, or fractionMake sure answers are completely simplified

Answer 1

As you can see in the picture, the graph shows a Non-linear function, therefore it is not constant.

The Average rate of change can be found using this formula:

$Average\text{ }rate\text{ }of\text{ }change=\frac{f(b)-f(a)}{b-a}$

Then this means that you need to divide the change in "y" by the change in "x".

In this case you know that you must find the Average rate of change over this interval:

$\mleft[1,4\mright]$

This can also be written as:

$1\le x\le4$

Therefore, the points you need to use are (as you can see in the graph):

$(1,1);(4,2)$

So you can set up that:

$\begin{gathered} f(b)=2 \\ f(a)=1 \\ b=4 \\ a=1 \end{gathered}$

Substituting values into the formula and evaluating, you get:

$\begin{gathered} Average\text{ }rate\text{ }of\text{ }change=\frac{f(b)-f(a)}{b-a} \\ \\ Average\text{ }rate\text{ }of\text{ }change=\frac{2-1}{4-1} \\ \\ Average\text{ }rate\text{ }of\text{ }change=\frac{1}{3} \end{gathered}$

The answer is:

$Average\text{ }rate\text{ }of\text{ }change=\frac{1}{3}$