Question

The average rate of change of the function $f\left(x\right)=x^2$between $x=1$and $x=5$is

average rate of change$=\frac{\boxed{}}{\boxed{}}=$

Short answer

The average rate of change$=\frac{5^2-1^2}{5-1}=6$.

Step-by-step solution

Given Information

The given function, $f\left(x\right)=x^2$

The average rate of function over the interval,

$x=1$to$x=5$

Evaluate average rate of change

Substitute $x=5$

Substitute $x=1$

$$\begin{gathered} f\left(1\right)=1^2 \\ f\left(1\right)=1 \end{gathered}$$

Average rate of change of function ,

role="math" localid="1650277166710" $$\begin{gathered} =\frac{25-1}{5-1} \\ =\frac{24}{4}[reducefraction] \\ =6 \end{gathered}$$