Answer
The average rate of change of $f\left( x \right)=6x$ from ${{x}_{1}}=0\text{ to }{{x}_{2}}=4$ is $6$.
Work Step by Step
Consider the provided function $f\left( x \right)=6x$.
The value of the function $f\left( x \right)=6x$ at ${{x}_{1}}=0$ is
$\begin{align}
& f\left( 0 \right)=6\left( 0 \right) \\
& =0
\end{align}$
The value of function $f\left( x \right)=6x$ at ${{x}_{2}}=4$ is
$\begin{align}
& f\left( 4 \right)=6\left( 4 \right) \\
& =24
\end{align}$
The average rate of change of $f$ from ${{x}_{1}}=0\text{ to }{{x}_{2}}=4$ is
$\begin{align}
& \frac{\Delta y}{\Delta x}=\frac{f\left( 4 \right)-f\left( 0 \right)}{4-0} \\
& =\frac{24-0}{4-0} \\
& =\frac{24}{4} \\
& =6
\end{align}$
Thus, the average rate of change of $f\left( x \right)=6x$ from ${{x}_{1}}=0\text{ to }{{x}_{2}}=4$ is $6$.
